E.W.
I am truly sorry for the situation your ex husband has put you in. My parents divorced when I was very young and mother ALWAYS said horrible, nasty things about my father. I saw him on his regular visitation days and he has always been there for me. Despite the nasty things that my mother said about my father I always knew better. I knew that he was not the person that my mom made him out to be, she is just a mean bitter woman. What I am getting at is people will know the truth just by the way you act, react and deal with situations. Your son, the daycare worker, and anyone else that she slanders your name to will know better. I will confront your ex husband about what she is saying just from the standpoint that if he has any respect for you as his sons mother that he should handle his woman. I would not give her the dignity of a reaction because I am sure that is what she wants.
As hard as the break up was you obviously "got rid of" a pretty crappy husband. (Anyone who cheats emotionally/physically on their wife has to be a pretty crappy husband) The good thing is now she has your old problem, once a cheater always a cheater and I am sure he will cheat on her.
Just know that you are doing everything for your son that you possibly can, and you are trying to make the best out of a bad situation. Good luck!