what about getting a nanny that is there a lot even over nights and try to get the courts to give you half of day care? These are the jerks that need gold diggers to go after them.
If he is violating the court order go with out a lawyer and have the judge decide. For next yr in January email, get the money etc way before sign up. Or have him go to sign her up with you, . File the court papers with plenty of time before the activity needs money.

As far as sports and activities I would not put my child with his personal friend that is just setting you up to talk about you and make you and your child uncomfortable.