Can my ex prevent our kids from being around the man I am dating even after we get married?

Yes I have a question regarding something that was in my divorce. I have 2 children with my ex and he is the type where I'm his first love and he doesn't want anyone else but me. Well, we share 2 kids together and the guy that I'm dating has a little background. He has to register due to sex offender juvenile I believe but he has no stipulations. Well my ex has made it impossible for my kids to be anywhere around him while they are in my care due to they showed more interest in him than they did their dad. I was wondering if me and the guy I'm with ever happen to get married, could my ex still prevent my kids from being around him? This is something I really want to know so could I please get something soon.