is a verbal agreement binding in n.y.?

We are going through a divorce, and my husband made a verbal agreement with me, that if he was able to claim our children on taxes, he would split the money with me. He doesn't pay support, I have to re-file a petition for support, because he didn't come to court last time. I have full physical and residential custody of our children, and he doesn't help financially. I'm filing for the divorce. He cheated and then left us to be evicted from our house. I need this money, and he knows it, but he's being mean about giving it to me. Can I do anything about this?