The change in advice in the latter part of this thread is wise, and spot on.
I'm sorry OP, but the only reaonable and sound advice anyone with any sense would give you is to get a lawyer, forget the counselling, and get rid of him. He's a serial cheat. He WILL NOT stop being one - it is a fundamental part of who he is. And you have your children to think about... I would think very carefully about the example you set them now. Factor in the almost certainty that this OW isn't the first person he cheated on you with - and the path is obvious.
As for your actions years ago - everyone makes mistakes. Some worse than others. We've all done something in the past that we're truly ashamed of. The trick is to learn from it. Most of us do, and are better people for it. Just as you say.
Now, stop and think and apply that bit of life-learning, that wisdom you have now gained, to your H. Think how guilty you still feel now about how his wife was treated. Clearly, he never, ever, felt the same...despite the fact that she was his wife, the woman he made love to and married and made promises to and had dreams with. She was just a name and face to you, and you were - and are-guilt-ridden by your actions. Him? Nah. Not a flicker. How do I know that?
Fast forward to now. He's done it again, with aplomb. Because he learned nothing all those years ago. To him, there was nothing to learn. His deceit and cruelty touched him on no more than a completely superficial level... because here he is, years later, being happy to do the same thing. He's ok with infidelity and the pain it causes, because deep down, he doesn't give a shit about anyone but himself. Including his own, now distraught, DD - whose innocent childhood years he's just pissed all over.
His feelings for you are of the same calibre as they were for her, aren't they? Let's examine it. You've been together many years. You have children. Nope, makes no difference. He can happily shit on you the same way he shat on a woman he'd promised to love only a couple of months ago.
His actions here weren't a 'slip' - it's a year and a half of cold calculating deceit, bringing her into your bed - there are no words, really. It's proper, life-destroying deceit - just as he did to his poor first wife.
OP, this man is a liar, a cheat, a selfish, unreliable shitbag. He just is. There is nothing to counsel, there is nothing to 'work through'. The only thing you will find yourself working on is how to now build a life where you can lie to yourself, and lie to your children, for the rest of your life. You KNOW what this man thinks of you, and any other woman unlucky enough to share his bed. So act on it, and get shot of the nasty little cheat. Your DD will be proud.