I have to say when I read the title of this question, i was reluctant to click on it, thinking that this was another question about how to get the husband to stop talking to the Ex-wife. Im glad I checked though, because when you add a kid into the equation, it really helps to put the whole situation into perspective.
I would say that you have to be the better person in this situation. You've got to be nice to her in ways that she would never be nice to you. She has already stemmed resentment towards you and she expects that behavior back from you. If you give her what she wants in the way of hostile behavior, it will give her the perfect excused to feel that her child is not safe in a home with you, even though she knows she is manipulating the outcome that way. It is human nature to react to hostility with hostility.
What you could do is go out of your way, and do something like send her flowers on her birthday or something. Chances are that at first she is going to get angry, not because she got flowers, but because she knows you're not on her level where she wants you to be. This really could go either way, but at least you can say that you tried to make peace with her.
I cannot guarantee you a successful outcome, but I think you will feel better about the situation, and if it doesnt turn out ok, then you will not be the one coming out of the situation looking like a fool.