My question involves criminal law for the state of: Illinois

I live in Illinois, I have a daughter and a boyfriend who has a bogus sex offender charge against him. Can my daughter's father restrict me and my daughter from living with this man? My daughter’s father and I have joint custody and I have primary placement. She lives with me in Illlinois and he is homeless living in Wisconsin.
My boyfriend was charged with "raping" a girl that was the same age as him when they were both under 18. He was charged with a third-degree class H Felony. I know he is a fun and loving person and this is ruining his life. I know he means no harm to me or my daughter.
He is currently on probation and will be for the next year. When he gets off probation is it illegal to be with him when I have a daughter? What can my daughter's father do about this issue? What are my rights?