Some questions:
1. How old is the girl? I get the impression that she is between 14 and 16.
2. How is she doing academically? Never mind her attitude, how are her test scores?
3. You say her parents are rich. Does the school depend on them for major support? Could it be that the girl thinks that she can get away with anything because Papa hat gelt and the school needs him? Does Papa have the same attitude, I.E. You have to keep/accept my daughter or I’ll walk?
If the answer to #3 is all yeses, what is happening is that you and the school are being bullied by an obnoxious girl raised by obnoxious parents all of whom think that their wealth and social status lets them do as they want. The only effective way to deal with bullies is to stand up to them. I strongly suggest that the girl be summarily tossed out of school and if Papa says he’ll take his money elsewhere, tell him, “Go ahead. And don’t let the door hit you on the way out!”
Be certain that the One Who Provides Sustenance to All will see that the loss of revenue from this schlemiel will be made up by others and, who knows, maybe finally being stood up to will have an educational effect on them. You’re a teacher. Not all lessons are taught in a classroom.