You say "his kids" I assume he has been married before, or if not, the relationship then was strained, it ended and so you have his children and one of your own.
Perhaps he came into this marriage with baggage as well as the non-understanding of what constitutes a relationship, can you change either of those things in him even with councelling? I don't think so.
He's done it before, you were fed up and so you had an affair, that created him to deny the baby was his and cause emotional stress for 3 years, if not still.
Now, you feel he's done it, doing it again..
Can't you see the rollercoaster you are on?
Instead of fighting for your marriage by means of approaching not only another woman thought to be part of a situation but her husband and then threatening to tell their boss?
Threatening someone is not cool...and it's not going to stop your husband from cheating if that's what he wants to do.
Both of you sit down and tell each other why you cheated on each other, why you love each other, why you don't think you'll ever do it again....If you can't do that, there is no hope, you don't have a marraige, just a piece of paper.
It's funny, you say he cheated before, maybe you didn't have proof, maybe you did then... You tell him you did and he spends years avoiding his child, whereby a paternity test would clarify, could have clarified.
If he acted that way? In my opinion, he's never ever going to forget, never going to see you as a "wife to have and to hold till death do us part", as he is never going to trust you either..and he will have the thought in his mind of "care" not, she cheated on me.