Does she also have friends at the prep school ? Do you ever invite her to have them come home with her on a weekend ? Do you have an opportunity to talk to a guidance counselor, so you can get a more whole picture of what is going on ?
She's 16. My almost 16 year old is the most centered teen I know, but she, too, is exhibiting some of those, "parents are stupid" kinds of things. They are setting themselves apart from their parents, and trying to live that way. . . .just keep a very long tether. As long as she is trustworthy, allow her some leeway to be different from you, and always welcome her back. She won't be there forever. (yeah, I need to hear my own advice -- thanks !)
And then with school ? Why don't you tell her that you've paid for this year already. If she gives it a good try, works at making friends, and still isn't happy there, you will consider having her come back to her own home district for her jr and sr years. . . She can even shadow her home school in Feb or March -- it won't hurt anything, and it might open her eyes. She might find that the school she's at is MUCH better and more interesting. You never know.
the other thing is that kids are online so much, that she can talk to her friends when she's away at prep school anyway -- so she can have both worlds then, whereas, if she comes back home, she will be pretty much just with one group of friends.
and, honestly, she's had a good start to high school. Usually the smart kids will excell whereever they go to school. If she comes back home and is happier, and continues to get accolades at school, there are worse things than that in life. . . . :-)
On the other side, be sure to get her active in the decision making process. . . . Let her know it's a family decision (you, dad and her) Make written lists together of what you are looking for in a school, then judge each school on those qualities, and let her judge, too. So you each score both schools. Teachers, accessability of teachers, friendliness of students, feeling of "home", and quality of education, kinds of courses -- for instance, our daughter is in a magnet school (living at home) that she chose, cuz she hated going to our local school, and she is taking German, which isn't offered here. She's also taking an AP English course which is VERY intensive, and I'm impressed that she's doing it as a sophomore. Homework has definately kicked up a notch over last year which was twice the homework the local kids have . . . but she doesn't ever want to return, so she sticks with it. She has some good friends from our local district, but especially this year is finding some really wonderful friends where she is. And I'm increasingly happy for her . . . but her relationship with me ? Well, I have to bite my tongue a whole lot. daily. :-) I'm waiting for 18 when it begins to turn back the other way . . . . ????? . . . I have 2 adult daughters, 28, and 26, and both of them call home often, so I guess it really does go back to normal at some point -- I just don't really remember where that is !
Good luck, M., and hang in -- I gave my husband a quick version of your letter, and he said, "Are you writing to yourself today ?" I'm with you all the way on this one !!!