From reading your other posts, it appears to me that you have no reason to trust him. There are more than likely other actual affairs that he hasn't told you about and not just the "incidents" you're refering to. He's a slick Willie for sure.
Can you reconcile after an A? Yes, but he has to do the work, which it is apparent he hasn't done. I'd say give him an ultimatum. Either go get help, and give you total access to everything he is on, or he will have to leave.
Why are you afraid to make him look/feel bad? He's cheated on you without obvious remorse and done so repeatedly I'd imagine, and really has no second thoughts about it will make you or the kids feel.
Your WH has lost the right to have trust. He now has to earn every last drop.
However, personally, I don't know if I could. My WW isn't remorseful at all. The minute she (they) decided (decide) to commit adultery, there is no going back. One can no longer call themselves faithful, honest, one of integrity.
The least you could do for yourself and your children is to contact your pastor and lawyer. Have them help you sort this out.