For a start, she couldn't afford the pounds 350 a night. Neither, of course, could I; but it was I, rather than she, who became one of the few authentic Carnegies ever to grace the Carnegie Club. Skibo Castle is the former home of the steel magnate and philanthropist Andrew Carnegie and is now one of the most exclusive country clubs in the world. It has been manicured back to fin-de-siecle finery by the maverick entrepreneur Peter de Savary.
To mark the visit my sister had given me a Carnegie tartan tie. I have to tell you that we Carnegies - my paternal grandmother was one - are a distinctly second division clan from Fife and Angus with a rather tatty tartan to show for it: all dirty reds, blues and greens with a splash of garish yellow. Only Andrew Carnegie, the Bill Gates of his day, and Dale Carnegie, author of How to Win Friends and Influence People, have ever grabbed the headlines for the clan.
After dining by candlelight I revealed my true colours, brandished my tie and publicised my pedigree. A suave chap who bought old masters for the royal families of Europe yawned and drained his tumbler of Glenmorangie. James the butler, more Jeeves than Jeeves himself, was at his side in an instant. "May I freshen that for you, sir?"
After his fourth whisky he was turning back the clock to his first visit to Skibo. "I was introduced to some oil tycoon and his wife, who were quite charming. Then I was greeted by another dignitary - it's more than my life's worth to tell you who it was. She shook my hand, and said: `And how rich are you?'" My informant was all set to let drop some titbits about the Windsors when his glass of whisky lurched and his head collapsed on to his chest.
Surely this wasn't quite what Andrew Carnegie, a teetotaller (he gave his staff a 10 per cent bonus if they abstained), had in mind when he invited VIPs to his grand Scottish pile for elevated chat: Rudyard Kipling, Edward VII - he pinched some plumbing ideas for Buckingham Palace - the Rockefellers, Lloyd George and Sir Edward Elgar. As the log fire crackled and a Labrador rearranged itself over my feet, I realised that today's pre-millennial arrivistes cared little for the legend of the Dunfermline weaver-made-good. And they certainly didn't care about me, a down-at-heel Carnegie groupie.
I was woken the next day by the sound of bagpipes outside my window, the ritual that propels sleepy club members into another round of over- indulgence. Over porridge I met a second-hand car-dealer and his wife from Burnley. For all our efforts to lend a little class to the proceedings, our chat was more in keeping with a Blackpool b&b. Perhaps we were trying too hard.
Outside on the lawn the falconer had appeared, as he does every morning at breakfast time. We watched as the bird of prey shot upwards, circled, speared down like a jet fighter, screeched to a mid-air halt and dropped on to the outstretched hand.
The hosts at Skibo hover without being intrusive, tending to your every need, more attentive than a hotel but seeming less so. Studied informality is the order of the day and staff dress reflects this: sensible tweed jackets, country shoes and tasteful neckties - and that's just the women.
A tight schedule had been arranged for me so that I could sample the range of activities. Archery and clay-pigeon shooting are also on offer but I jumped into a Range Rover - one of a fleet of vehicles that ferry guests around the 7,500-acre estate on the shores of Loch Dornoch - and was whisked away to the golf course. Unfortunately the magnificent links, complete with a seal of approval from Greg Norman and Nick Faldo, were frozen over - but young Jodi gave me a lesson instead and in half an hour had cured me of my four-year-long affliction of slicing off the tee.
The majority of the 550 Carnegie Club members come for the golf, but not at the end of the December. My companions were gourmets and hedonists who hugged warmth and huddled around log fires. The exception was David, the rosy-cheeked property developer, who sported plus-fours whatever the time of day and whose band of dogs scurried in his wake. He'd just been out deerstalking and had "nabbed four beauties". "Marvellous, marvellous, really got the adrenaline going," he said. I had noticed there was venison on the menu that evening.
At the turn of the century Andrew Carnegie built a heated, marble indoor swimming pool, and it is still there today, one of the loveliest features of Skibo. But the water was cold, perhaps, as a sneering affinity broker told me, to maintain it at the temperature the hard man of steel preferred it - to preserve authenticity. To it has been added a luxury spa with sauna, steam room and gym. I opted for a massage from Margaret, whose expert touch was soon sorting out the knots in my back.
The light was fading and it was time for afternoon tea. The tradition is that almost everything is included in the price - drinks, meals, golf, transport from the airport. Anyone is entitled to make one visit but cannot return except as a club member, for which they have to submit an application. Some 65 per cent of members are Americans.
It is no secret that the roster has included Jack Nicholson, Michael Douglas, Tom Hanks, David Jason, Jeffrey Archer, Lenny Henry and Dawn French. On good days a line of private jets can be seen parked up at the airport, 45 minutes' drive away.
About 90 per cent of the furniture at Skibo was owned by Carnegie, and it has been wonderfully preserved. There is a superb library, dungeon, grand piano on which Paderewski played, an organ, stained glass windows, Britain's first lift and a stunning range of suites. Mine had its own circular stairs and turret, my friend's bathroom contained a pool table. Throughout the house the door handles are set low, a design feature demanded by the man himself because he measured only 5ft 2in.
On the last day I put my Carnegie tartan tie on expecting to slip quietly away without anyone noticing - and indeed no one at Skibo did notice. I wasn't spotted until I got to the airport. "Now I recognise that tartan," said the wily baggage handler. "You don't see many of them in these parts. Not many real Carnegies up here." Now, Auntie Jean would have enjoyed that.
Robert Nurden was a guest of the Carnegie Club, Skibo Castle, Dornoch, Scotland IV25 3RO (tel: 01862 894600). Rooms cost pounds 550 per night for a double, pounds 350 per night for a single. He flew from Luton to Inverness with easyJet (tel: 0870 600 0000). Return flights cost from pounds 48. British Airways (tel: 0990 444 000) flies three times a day, weekdays, from Gatwick. Return flights cost from pounds 79. London to Inverness by train costs from pounds 30 (tel: 0345 484950).