Annie , how about somewhere within 5 miles of Chiddingfold in Surrey? Lovely area, Witley station means it's 45 mins to Weybridge and 55 mins to an hour in to Waterloo.It's a lovely area around there, very pretty, I'm positive there would be 'horsey homes' (or stabling) opportunities there.
I would never worry about renting somewhere in your circumstances. Better off renting somewhere for 6 months in a prospective home location and finding out you don't like the place. Than spending £500k on a house, then finding out you don't like the place!
Or you could carry on doing what your doing now. As Mr Two Bears business to contribute to the rental cost, as work is dictating where you have to live. You'd have to look at the tax implications of that of course (benefit in kind etc). Then that means you can keep your home in Yorkshire and that makes things easier for your daughter.
How about putting a marker in the sand for everyone "we'll sell up in Yorkshire this time next year....". Spend that year really working at finding a new area in the South where you want to live. Having lived in Godalming and recently been back there it reminded me how lovely that area is. It did remind me how expensive it had become though.
It was nice to get home to Somerset