In turn, Judy recalls a small, loud, barnstorming baby who grew into a similarly tempestuous child who hated losing to his elder brother, Jamie, at Monopoly (or anything else) so much that he would overturn the board, pieces flying, when such an outcome looked likely. But for all the tantrums, the bond between mother and son remains live and powerful.
After almost every point during his Wimbledon matches, Murray turns his eyes towards the players' box where his mother, girlfriend and team of coaches sit. Judy used to try to disguise her roaring, fist-clenched support by restricting herself to split-second responses and lapsing into fake composure. Her son's fame has put paid to that. Now the cameras don't miss a thing. She admits watching him is like a cross between "seasickness and a heart attack".
She utterly refutes the accusation that she is a classic "pushy" parent. "Anyone who knows me can tell you I'm not pushy at all. I don't try to dominate the lives of my sons. I've always been a believer that if you make a decision yourself and it's a mistake, you're going to learn much more."
Murray backs her up. "I can't remember the last time I was in an argument with her," he told me. "Genuinely can't remember. I never slammed a door. Never said I hate you.' I think my mum's the only person who gets me, who understands me really well."
Partly this stems from Judy's own experience on the women's professional tennis tour at the age of 17, a hard period of penury and unhappiness.
Seriously homesick, she abandoned the plan.
Marriage and motherhood subsequently replaced becoming Scotland's answer to Chris Evert, but she still went on to win 64 Scottish national titles. Perhaps there is a complicit delight in seeing her son reach the sporting heights that eluded her.
Their relationship is perhaps best summed up by a Christmas card that Andy once sent his mother that unashamedly thanked her for "always believing in me, always supporting me, always letting me make my own decisions but most of all being the best Mum in the world". She cried.
He looked at her in teenaged disgust. "What are you crying for, stupid woman?" he said, baffled.
If his mother and her deep understanding of his intractability has been the prime influence in his life, then others have certainly come close.
Grandmother Shirley, Judy's mother, is a formidable matriarch. Andy and Jamie were partially brought up by "Gran" in hometown Dunblane, allowing Judy to concentrate on earning a living after her divorce from the boys' father when Andy was 12. Gran was serious about discipline, baking shortbread and driving very, very cautiously to tennis practice to the mocking hilarity of her grandsons. Her husband, Roy, is a former Hibernian footballer.
Both grandparents were proudly present at Wimbledon last week when Scotland's Andy Murray bowed with magnificent formality to Great Britain's Queen on the Centre Court, finally scotching the pervasive reports that he was a foul-mouthed, anti-monarchist rebel.
Meanwhile, following the break that occurred after the US Open last year, in November, girlfriend Kim was back in Murray's life by the spring. Some wondered how she had managed to tolerate the predominantly male aspects of his entourage — the dressing-room antics and endless games on PlayStations — for so long before they took their toll, but she has always identified Murray as wry, bright, affectionate and perfectly capable of reading books, even if they were mainly Harry Potter.
Their loyalty to one another runs deep, partly, as Murray once explained, because he is alive to the pain caused by couples splitting following his parents' divorce. Last summer, he and Kim moved into their new mansion in Surrey's footballer-belt, complete with terrier Maggie, who promptly swallowed a mouthful of pebbles and needed an expensive operation. It was perhaps a reminder that perfection is a state rarely sustainable.
This year has been a time of realignment. Having cried on court with disappointment and frustration following defeat by Roger Federer in the Australian Open Final, Murray suffered a dip in form that has lasted almost five months. But Wimbledon 2010 seems to have changed the wind in his favour. Kim is back, he has reached his allotted place in the semi-finals, and if he is granted a tilt at the men's singles title on Sunday, the first British man to do so since 1938, there will be three women (and a dog) who played their part.
