For the youngsters it was a living geography lesson that gave them a streetwise determination and independence way beyond their years. For David it was a long-held dream come true and he relished every single second. But for Kate it was at times nothing short of a nightmare that threatened literally to drive her mad. The very project that had promised to bring the couple even closer together came close to catapulting them apart.
A decade later, there is a sense that they are still coming to terms with their journey and the effect it had on their relationship. "I wasn't as understanding as I could have been with Kate," David admits now, "but I had a lot on my plate and I wanted her to get on with things."
I had half expected New Age hippies. But David, an ecologist, is immaculately presented; in his late fifties he could be a decade younger. A carefully laundered green and white gypsy neckerchief is about the only discernible symbol of anarchy. Kate, 48, a former nurse, is carefully made up and quiet, although she claims she has become less shy and more resilient since her trip.
It's little wonder. During their journey they coped with flying bullets as Yugoslavia disintegrated before their eyes, witnessed the break-up of the Soviet Union, the worst winter Kazakhstan had seen for 30 years and fought a potential eight-year jail sentence in Mongolia after drunks tried to steal their horse and one later claimed to have been blinded when Eilidh fired her catapult over his head.
Kate had other, more basic difficulties. "It's easy for a man to stand against a caravan and have a pee," she jokes now. "For a woman it is quite different - having to walk miles to find somewhere where you didn't feel in full view was tough." Sex virtually went out the window and personal hygiene was compromised. She battled against constant tiredness and depression (later diagnosed as a thyroid problem) as she struggled to live in a cramped 14ft by 6ft caravan for months on end without running water, electricity or a toilet.
The pressure finally took its toll. Kate was driven to abandon her children for the first time in her life and returned to the UK several times. While away from them she pined dreadfully. "I gave myself a hard time about wanting to pull out which made it worse. It was incredibly upsetting hearing their voices on the telephone." But back by their sides she felt a failure. "I felt I could no longer stand it and that I was probably making life hell for David and the children. I didn't want to spoil the trip for the others." For years she traipsed back and forth across huge land masses, leaving and rejoining her family when she could once more cope. Yet there were times when her link with home was a blessing. During their trouble in Mongolia she campaigned in the UK for their release.
Unlike his wife, David considered quitting only once, in North Dakota, after the death of their carthorse, Traceur, from a brain tumour. The rest of the time, through often horrendous difficulties, such as when he and the children fell sick with headaches and fever and Traceur fell lame in Kazakhstan, with Kate at home, he had to keep going. "We had limited food supplies, an extremely lame horse and the boys had wildly fluctuating temperatures," he remembers. Eilidh managed to find a vet and a doctor in that alien land. Like boomerangs, the children - who learnt to haggle and communicate often without language - always found their way back to base.
Their resourcefulness was a constant source of pride. In Russia they ate kasha (buckwheat) and jarred meat, which was usually reserved for their dogs; in Mongolia they slaughtered and ate seven sheep. Two of the children came to hate mutton so much they turned vegetarian. But David also recalls them playing hopscotch with kids in Mongolia, none of them speaking a word of the others' language. Says Kate: "I am still amazed at the hardships they endured. They carried on without any complaints. I remember going back to Kazakhstan and Eilidh looked totally different. She had lost her puppy fat and was so slim, and very independent, thoughtful and caring. Fionn looked emaciated - he was fussy about food and there wasn't a lot to eat."
Before their departure, the Grants had spent a long time researching self-teaching methods for the children and contacted the charity Education Otherwise for advice. Without television and other distractions, the youngsters educated themselves. "They did school work when they felt like it. It was terribly anarchic but it worked," says David. Torcuil regularly scored more than 90 per cent in his English. At 19 he is now studying for an HNC in applied ecology at college and hopes to go to university. Fionn, 14, has just had a glowing report from Webster's High School in Kirriemuir. His great passion is for basketball which he cultivated in the US. Eilidh, now 17, is working in a racing stables.
David, meanwhile, wrote a book about his experiences, The Seven Year Hitch, in Switzerland during the couple's estrangement. (They have since reunited.) He has had plenty of time to reflect. So what made them reach for such an ambitious goal? "No one had ever done it and we wanted to be the first," he smiles. And the transport? "We needed a vehicle that wasn't going to break down in the middle of the Gobi Desert. Besides, horses, the caravan, children and dogs were a great combination. Everybody loved it."
Indeed they were often perceived as a travelling circus. In Italy a man asked for tickets for their show. Others saw them as gypsies, the bearers of good luck. In some countries, like Slovenia, they set down roots. "We stayed for a whole winter," says David. "I played the bagpipes at their independence ceremony. I loved their way of life."
On their return, with David in Switzerland, Kate and the children lived for a while on benefits. She went on to buy their cottage with an inheritance and is now working as a care assistant in a nursing home. She would like to do another trip but perhaps to South East Asia - and not with the family. "I don't regret the experience but I do regret leaving them to come home. I never felt like leaving for good, even though some friends thought I should get a job and wait for them to come back. I am far stronger than I was."
David concedes they have a lot of bridges to build: "Our relationship is on a different footing but we are still here." Kate lifts her eyebrows at the irony. Concluding The Seven Year Hitch, David writes: "Once this book is with the publishers, it will be time to organise the next expedition. But I may have to paddle my own canoe." Only time and a lot of healing will tell.
`The Seven Year Hitch', published by Simon & Schuster, pounds 16.99.