So sorry about the schools. Rejection is hard, for whatever the reason.
Don't get too hung up on extraversion, though. That's a personality trait that's hard to change. Focus if you'd like on behaviors, which you can change. You can't make an introvert want to party, but an introvert can learn to be assertive, respectful of social norms, and confident.
Also, I'm not entirely convinced that you can't move along the extravert-introvert spectrum in life. Without psychotropic drugs, that is!
I hope you do find a good place for your daughter, where she can develop confidence even as an introvert.
