My strong advice is to keep him away for now.
In the first place, this really is all about him.
But the fall-out of his behaviour has hit you hardest, not him.
Yet he's making this er... all about him
Together with some convenient blaming....of the "I wouldn't have done this if our marriage had been better" variety.
Bollocks he wouldn't.
He did this because he could and because he got the opportunity. He was quite prepared to carry on with you in the dark and him unilaterally withdrawing from your marriage. He was prepared to let you carry on looking after his kids and providing domestic service, first while he continued having an affair and then when he got found out, while he dithered between you and the OW.
He's incredibly manipulative. Those tears are for himself and are self-pity, not contrition for what he's done.
If you let him walk back in and take one single bit of blame for his behaviour, you will live to regret it for the rest of your life.
He didn't have to do this. As another poster has said, I bet a lot of the 'problems' in your marriage were just your reactions to his selfishness/self absorption. You can bet your house that this got worse as soon as he clapped eyes on the OW and had her lined up as affair material. That's when doubtless the really shit behaviour and selfishness started, but probably because he was always something of a selfish, woe-is-me-I-work-so-hard sort of manchild, it took you a while to notice things were suddenly much worse than normal.
He'd still be having the affair and keeping you in the dark if you hadn't found out.
Let him live with those consequences now. Watch what he does when you don't back down and when you refuse to take the blame.
That will be the measure of the man, not some pyscho-drama he's staged because he's been brought to the front of a school assembly and named and shamed and feels sorry for himself.
Of course, all this drama has neatly got him off the hook of ever having to give you any proof that things are all off with the OW, which is of course just what he intended.