I know this can be a tough decision for everyone involved. Just recently my son returned to live in the US after spending nearly five years here with me in the UK. He never fully adjusted to living in the UK and wanted to return home. Unfortunately, things didn't work out so that he could permanently reside in the US (the ex is a real work of art), so he's back with me again.
If I were in your shoes, the one thing that would concern me would be schooling. Students over here take something called GCSE's during the school years that they are 14-15 and 15-16. In a normal school, that's two years of intensive studying in their chosen subjects. In the last year, they will sit their GCSE final exams, which can ultimately determine whether you can progress on to A-Levels (a higher form of education). After A-Levels, you could then progress to university.
Based upon the age of your daughter, she would be entering the second year of GCSE studies (at the start of the next school year) if she were to move to the UK. This would mean that she would miss one full year of GCSE work. And make no mistake about it, there can be huge differences in class work between the two countries.
Of course, there are ways around the two-year GCSE studies. Rather than going to normal school, your daughter could go to a local college and take one-year GCSE courses. This wouldn't be in a 'normal' school, but a more adult one, almost similar to a community college in the States. This is the route my son will take because he has missed parts of the two-year GCSE studies that he would receive in a normal school.
My gut reaction to your situation would be to allow your daughter to remain because of the schooling situation. It may end up being easier on her in the long run to stay in the US. But, I recognise that every situation is different, and it could be that she would benefit from an education in the UK.
I'd highly suggest that you do a search on the net about GCSE's and difference between American and UK education, just so you and your daughter are fully informed and can make the best decision for you both.
Good luck!