Based on you narrative, this girl is a constant source of disruption and defiance. Tell me. Is she a new student or has she been in this school since early grades? if she has, has she always been disruptive or is this relatively new behavior? I’m surprised that the school has tolerated her behavior for so long. Would the school suffer loss, either financial or social if this girl were kicked out?
Again, based on you narrative, I don’t think that this girl is acting out because of unanswered hashkafic needs or emotional problems. I still believe that she is behaving so because she can get away with it and has for a while. She is a bully and the more she can make you feel inadequate and “try to reach her”, the more satisfying a victim you become.