I have a friend who started a charter school. He said the reason charter schools do better is nothing to do with teaching, it is that they are allowed to kick out the trouble makers.
Public schools are required to take all applicants. In the past my town had a special school where you got sent if you were caught with drugs or other major infraction.
Maybe try the Danegeld approach? If a student is good all week give them $50 on Friday.