Can my boyfriends ex go to court to stop me from being with his kids on his parenting time if I was convicted for domestic violence?

Absolutely your boyfriend's ex can obtain a temporary restraining order against you or even a permanent one if you were convicted for domestic violence.   Ultimately, the court places a huge importance on children's safety, and if that means you must stay away based on your history of violence, then that is what it will do. 

Further, the ex can even prevent the father from being near the children without supervised visitation if the ex believes you will join the visitation and convinces the court of the same.

Are you on parole or probation? If so, check your conditions because it may limit what you can do and if you get into any trouble, it may cancel out any probation or parole you may have.