Do not lower yourself to his level. Keep everything professional as if he was your (jackass) business partner. He is doing this because he is hurt and does not like himself. He will move on, the pain and hurt starts to fade after a couple of years. Appreciate that he is trying hard to be a good father. In fact, you may want to tell him how much you appreciate that your children have such a loving, responsible father.
In the old family book, a question is asked to a family psychiatrist..."What is the greatest thing I can do for my children" the answer was "Love their Mother"..........You may want to remind him of that. "