From what you have said here...it seems to me that maybe it wasn't called the bad girl chair, but that "bad girl" came from somewhere. Why did she bring it up in the letter if she wasn't refuting what she heard the teacher say?
Aside: this also reminded me of when I studied in Chile, and meant to tell a professor that I had really enjoyed her class and got confused and used "enojar" (to anger for non-Spanish speakers). It was a politics class and we had had some spirited debates. The professor was like, "umm, yeah, Freudian slip much?" lol!
Anyway--your dd sounds like an amazing little person, with some big challenges and lessons to learn. I hope the school can figure out how to accomodate her if homeschooling isn't possible.
