CM is right. You hold the cards right now. You get you a lawyer and tell him how she does and who she hangs with. Let him know that she is the one messing up the kids heads by not letting them stay on schedule.
Am I correct here or did I not read where you said sometimes on her days with them she leaves them at her parents house and goes and stays with the sex offender? If she does, bring that up too. It shows she would rather have her fun than take care of the kids. Do whatever it takes to help yourself.