THIS woman is in full bloom. That’s what I keep thinking as Judy Murray sits down at a table at the Cromlix hotel, Dunblane. Murray – who's arrived slightly late after visiting her mother in hospital following a hip operation – has a distinct glow to her. She smiles frequently, and it’s a charming, youthful smile, devoid of the ferocity that's so often captured on camera. Some shortbread arrives. “Not as good as my mother’s,” she quips, with a brief chuckle.

At 57, and recently awarded an OBE, Murray displays all the signs of being in the full flow of some kind of blossoming. Just visible above the neckline of her jumper are the small, black ink legs of her her new spider tattoo – an act she did purely for “herself”. It's the spider Murray refers to in her new autobiography, the spider Robert the Bruce saw struggling in a cave, which represents perseverance and the rewards that can come from relentless effort.

As the mother of tennis stars Andy and Jamie, Murray's story is a good example of how “anything is possible”. “I mean," she says, "who would have believed, years ago, we would have had two Wimbledon champions from Dunblane, or even from Scotland? Nobody would have believed it. And that wasn’t the plan. The plan was just that the boys like tennis, they’re pretty good, they’re young, what does the next stage look like?”

Step by step, in other words, to the very top. But, her message goes, it’s important to start children young; get them outside instead of sitting on their mobile screens most of the day; get them just to learn through play.

The blooming is there in the story she tells about a woman who came up to her in the street and asked for her autograph, then looked at it, and said: “That’s a lovely signature. Mine’s inedible.” Then she follows it up with a laugh of delight.

It’s there when she speaks of making more time to spend with her grandchild Sophia, daughter of Andy Murray and Kim Sears, and with her friends. It’s there in her clear enjoyment in appearing as guest judge on The Great British Menu or the show All Round To Mrs Brown’s.

All of this is revolutionary. “Up until about five years ago, you would never get me to stand up in front of people and speak," says Murray. "It would terrify me.”

Her book, Knowing The Score: My Family And Our Tennis Story, contains countless reminders of the rough ride Murray has had in the public eye, caricatured, dismissed as the apron strings hampering Andy Murray, as simply the mother of two sons.

Murray was herself a champion, who won 64 titles in Scotland during her junior and senior career, went on to be Scottish national coach and then, in 2011, captain of the GB team for the Fed Cup (the women’s international tennis competition).

Though she has done more, arguably than anyone else, save her sons, doubles champion Jamie, and singles legend Andy, to promote tennis within Scotland and women’s tennis more widely, her sons' dazzling success has meant that for the most part she was, until recently, mostly just seen as Andy’s mother. Judy Murray: the woman in the players’ box, the pushy tennis mum. Even her ghost-writer, she says, commented on this. “Alexandra [Heminsley] said, ‘Everything you built up in Scotland has been completely subsumed by Andy and Jamie’s success.’”

When I suggest that the book seems like part of a midlife blossoming, it's clear she has thought about this. “Definitely,” she says. “There is a lot of research that says that the time when most women find their confidence is 52 and I would go with that. For me it was around then.”

Growing up in Dunblane, the daughter of tennis lovers Shirley and Roy Erskine, Murray learned the joy of competitiveness from her father, who above all did not want to be beaten by his children. Before university, she took a year out to play on the pro circuit. Later, she found work in the confectionery business, which was where she met her sons' father, William Murray, who was working for RS McColl. The couple settled in Dunblane and raised their two sons there, though in 1996 they separated and later divorced.

Several life events played a part in Judy Murray's recent blossoming. One is when she got the job of GB captain of the Fed Cup team in 2011. Another was a series of successes in 2012-13: her son Andy, winning Olympics gold in 2012, at the same time as she was captaining the women’s Olympics team, followed, in 2013, by Andy winning at Wimbledon. The third is her appearance on Strictly Come Dancing, a show which she says was one of the first things she did really entirely for herself.

What’s striking is that much of this shift has revolved around how she presents herself to the public. “For many years,” she recalls, "I turned things down all the time because I didn’t have anything to wear and I couldn’t afford to buy anything. There were all those years where, almost every picture you would see of me would be like this – grimacing or whatever.” She forms a fierce warrior frown – and it seems rather sad that she might now feel self-conscious about such an expression.

Then, on the evening of the 2013 Wimbledon final, she had an epiphany. Ushered into the changing rooms which had been filled with outfits for the Wimbledon ball, she chose the first dress she saw, a silver Jenny Packham, and after much encouragement, tried it on over her jeans. “I remember the pictures that came out of me in that dress,” she recalls. “I looked amazing in that dress. Because they made me look amazing. I thought, that’s the first really nice picture that I’ve seen of myself. And it made me realise that I could look nice, when I’ve got dressed up. And now I really enjoy it."

Our meeting at the Cromlix, the Murrays' grand family-owned hotel which Judy views as a contribution to the life and economy of the local community, takes place just prior to Wimbledon, where Andy and Jamie are playing. She has a system, she says, for deciding who to watch when both her sons are playing in a Grand Slam, one she developed after she found darting between the two matches agonising and unworkable. “I told them my system when I decided on it. I go to whoever starts first and then I stay until he finishes. If the other one’s still playing then I go on to that match.”

She still doesn’t enjoy the cameras on her, as she watches from the players’ box. At Queen’s earlier this year, she recalls, how a small remote-controlled camera – “a little Dalek thing” – was running backwards and forwards, occasionally halting in front of her. “I just want to stick my fingers up at it – and then that picture would be everywhere wouldn’t it? It’s so intrusive. It’s a really stressful situation being in the players’ box.”

Another key moment in Murray’s blossoming was when she gave a talk at an event which involved the motivational speaker Caroline McHugh. Murray remembers being so struck by McHugh's speech about “the art of being yourself” that she felt goosebumps. “I was sitting there watching her, thinking – ‘Oh my God, listen to her, imagine doing that, no notes.’” Afterwards, Murray joined the queue to meet McHugh. “And when I got to the front of it, Caroline went, ‘Ahhh Judy ... Hen, you are fantastic, I love your son.’ Honestly I was nearly crying.”

What McHugh had said had really chimed with her. “I said to her,” she recalls. “‘You’re so right about that not living your life trying to be what other people want you to be.’ You sit there and you think, people criticise you or something. And you think I’d better change, I’d better not wear that top, or I'd better not flap my arms like this any more.”

These stories are all the more poignant, given the struggle she's had to navigate the male-dominated worlds of tennis and sport. In her book, she recalls finally securing a place on a performance coaching course, only to be told by her tutor that he’d had a complaint from a man who had asked: “What could she possibly offer to performance coaching, when she's got two kids?”

Then there was the occasion when she went to collect the Scottish Young Player Of The Year award on Andy’s behalf, and sports journalist Tam Cowan was up on the stage presenting. At the time, she had no money to buy a dress for the event, which she hadn't realised would be quite so glam. When she got up there to collect the award, Cowan, quipped: “Could he [Andy] not have bought you something better to wear?”

“It was the worst feeling in the world,” she recalls. “I felt terrible anyway because I knew that I was completely underdressed. It made me not want to go to that sort of thing again.”

People often ask her how she felt about the criticisms that were thrown at her by the Strictly Come Dancing judges. Craig Revel Horwood said she looked like she had rigor mortis on the dancefloor.

“I say, ‘Are you kidding me? Have you seen what I’ve had over the years? Plus, [that kind of ribbing is] part of the show. If Craig Revel Horwood hadn’t absolutely pasted me, I would have been devastated. I would have felt hard done by. I know I’m sh**. But I was loving it. I was having a great time. And the audience were voting us in for a long, long time.”

Reading her autobiography as the mother of two competitive sons myself, I was struck by the fact that writing about both Jamie and Andy seemed to be a balancing act in itself for Murray – how to give them both their due, to not exacerbate tensions that might already be there.

“It’s hard,” she says. “I think the whole way through that has been a challenge. And whenever they had to play each other at tennis when they were young, I always wanted Jamie [the elder son] to win because it was just like the natural order. But it was very tough because all Andy wanted to do was beat Jamie, and still does.”

She tells a story about how two days after Andy won Wimbledon in 2013, he was at the house with Jamie, and within five minutes they had gone outside to play table tennis on the patio. “Five minutes later, Jamie’s in, throwing the table tennis bat onto the sofa from the doorway. ‘I’m never playing table tennis with you again, Andy,’ he says. ‘Aw, go on Jamie,’ says Andy, ‘I’ll play with my left hand.’”

Probably one of her toughest moments, in terms of sibling tension, was when Andy won his first ever ATP title in San Jose in 2006, and Jamie was playing the following day, in the final on the Futures circuit in Sheffield. “It was a huge thing for Jamie,” she says, “and we arrived and we were thinking – why are Sky TV here, they never come to these little events? And they were there because Andy had won this huge thing and the closest they were going to get was Jamie – and they completely ruined his day. I felt awful for him.”

In the absence of any path or system in Scotland to enable people to get to the top in tennis, the Murrays somehow, created one. The possibilities for Scots now in tennis are far greater than they were in Judy Murray's own youth. “When I was 17 and leaving school and wanting to have year off to play tennis before university, the dream of being a professional player would be a pipe dream. It would seem ridiculous because you’re Scottish. There’s no indoor courts. There are no coaches.”

Does she wish she’d grown up in a different era? Such as now?

She believes there is currently a groundswell, in terms of women in UK sport. “The more that our female sports stars and teams can achieve great things and build bigger profiles and be seen on TV ... It’s that whole 'if you can see it you, can be it' thing. Some of the biggest female athletes in the sporting world are tennis players: Venus and Serena Williams. And having Johanna Konta there now will help raise the profile and believability for girls in the UK.”

Don’t, however, make the mistake of using the word "feminist" with reference to Judy Murray. On being asked recently whether she is one, she recalls: “I thought, what even is that? I’m just a woman and I like speaking up for women and promoting the women’s side of things. It almost felt like the word was too strong. I thought, ‘Oh is it one of those things where I’m going to get into hot water, whatever I answer here?’”

Knowing The Score is a great book for parents, since it’s a reminder of two things. The first is that actually, Murray wasn’t the pushy mother she is sometimes portrayed as, but a woman who loved tennis and was passing on a family tradition to her children, teaching them by playing. The second is that actually, parents, through what they do not just with their own children and others, can be part of community transformation. There’s a grassroots element to the Murray story.

And it’s not just about any community – it’s also about Dunblane. The atrocity that left 16 children and one teacher dead, in 1996 at Dunblane Primary School, hovers ominously over some of the book's chapters. Andy, she writes, was with his class on the way to the gym when the shooting began in that room, and they were told to wait in the corridor. Jamie's class was in the Portakabin outside, and he recalls hearing a "pop, pop, pop". Does Judy Murray think that what they all went through then helped forge her sense that community had to be at the heart of things?

“I probably did become more community-focused after that. But I think the other thing with that was because it was such an enormous shock, and it makes you realise that you never know what’s round the corner. You make the most of everything and you just go for it.”

Her life is no longer, as it once was, “saturated" with tennis. “I do love tennis, but, for instance, on the radio the other day they were talking about the top five regrets of people who were dying. One of the biggest regrets was having worked too hard. You’re working so hard, life passes you by. And I think to some extent that happened to me.”

All the travel that came with her job meant her social life went for “a Burton”. She missed a lot of family occasions, and friends’ weddings. It’s still rare, she says, even at Christmas, given Andy and Jamie’s schedule, for the whole family to gather. “When we do that’s when I make them wear the Christmas jumpers and hats and everything. It doesn’t happen all that often, so it’s very special when it does. Not just for me, but for my parents, the cousins and everyone else.”

These, she says, are the “compromises that come with the territory”. Her own compromises are fewer now. Frequently she mentions doing things for herself. “I think,” she says, “now I’m getting to an age where you’re losing friends, you lose family, and you don’t know what’s round the corner. And you think, if I want to do something, or if I want to buy something now, or go somewhere now, I’m just going to do it.”

Knowing The Score: My Family And Our Tennis Story is published by Chatto & Windus. Judy Murray is at the Edinburgh International Book Festival on Tuesday August 15

* An error in the original headline has been corrected