What has he told you he was willing to do? He is the one that needs to do the work not you.
Maybe if you want to at least say that you did everything you can, give it a timeline. Detail specifically what you want to happen within a certain timeframe and see if he will stick by it.
Most importantly, I think you need to talk to a C or a minister/priest to learn forgiveness. that's where it needs to start. IF you can find the strength to forgive him, then you will have the strength to handle any shame or embarassment that you perceive as coming your way.
About him spending time with the OW child. Just remember that the child is innocent and deserves a father as much as your kids do. But do you forgive him enough to allow him to do that and extend that love to that child? You'll need all that strength to live without anger, shame and especially resentment.
M-43 W-40 2D - 9 and 5
Emotion, yet peace. Ignorance, yet knowledge. Passion, yet serenity. Chaos, yet harmony. Death, yet a new life.