I think you have to go through different immigration lines to get back into the U.S. (my husband and I have always gone to separate lines). I'm unsure how it works in the U.K., because we haven't tried it here, either. I kept my maiden name when we got married, so our passports obviously have different last names on them. I know that will be a hassle with immigration on both sides if we try to go in together. Regardless, we're going to try next time.
My husband and I have alternated using driver's licenses to rent cars in the States. I know for sure that Enterprise will accept a non-U.S. driver's license, as my husband used his U.K. license last Christmas to rent a car, while I was just briefly asked to show mine--it was understood that either of us could drive the car. (Make sure of that last bit, though, before you rent. They may ask you to show your license, as well.)
I hope that helps.
Suzanne
P.S. I've always found the people at Enterprise to be very polite and accommodating. I can't speak for Thrifty, though, because I've never used it.