Blimey Andrew, do you really want this person as a customer? If its financially viable then I guess you have no choice, but really.
I know none of us turn work down if we can help it, but sometimes we get a 'feeling' for an iffy client, hopefully your client isnt one of them?
I had one a couple of months ago and she was quite confrontational and even quizzed me why I was measuring the rooms. I said because it gives an accurate price for each area as its logical and fair - as opposed to plucking figures off the top of my head (said it in a really nice way).
She then carried on by saying that the 'other' carpet cleaner got out wood dye marks and coffee (oh and dog pee). When I explained the improbabilty - she got quite stern and looked at me with that look i.e. 'you clean - so all these marks should dam well disappear'!
I quickly made my excuses and got the hell out of there.
Anyway, I hope it all goes ok if your going back.
Cheers
Kev