Mike is right. I bet if you asked the ex-wife why the divorce happened, she would say he is a spineless wimp who never stood up for himself and she had to make all the decisions in the family. There's always another side to that coin.
If you live with your bf, and your name is on the lease, you have every right to speak up and try to limit her comings and goings. If you aren't on the lease, even if you live there, you have no place in saying who comes and goes. It's up to your boyfriend, and if he is not willing to set and enforce boundaries, then you need to speak with him about your expectations.
It sounds like you resent the place the other children have in his life. It's not up to him how much support he pays unless he is voluntarily paying more than is court-ordered. If his divorce decree states that he is obligated to pay for half the school fees, etc, then he has to pay them. And yes, if he just stops paying, he will be taken back to court.
You are in a precarious position. As his ex-wife, she under the law has more "say" in your boyfriend's life than you do. You are the mother of one of his children, but other than that there is no legal document binding you to him. Until the boys are grown (and sometimes even through college) she will continue to be a very active part of your life.
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