My ex-husband had an affair, admitted it, wanted to reconciled, and I divorced him as quickly as I could.
He knew going in an affair was a dealbreaker to our marriage, so it really surprised me when he started to melt down saying he wanted to reconcile, he'd never do it again, all of the things that you're writing here.
I'm sure there are lots of great stories of people who did have affairs and made their marriage work. But I wanted to add my own, it might give you insight into what your wife might be thinking (and obviously, I don't know either of you, but it's to give you perspective).
In a nutshell, the thing that drove me to the divorce more than anything else was that my ex put my life and the lives of our children in danger. He had sex with someone who could have had HIV, hepatitis, or any number of sexually transmitted diseases and could have put me at risk for that.
The OW he slept with could have been a mental case or had a dangerous husband or who knows what. Quite literally, he risked our lives, and I had to get away from it. I struggled a bit and have done my fair share of crying, and while it hasn't been easy - for me - there's not a day that goes by without be feeling grateful from getting away for someone who had zero respect for me or his family.
We have a civil relationship bc of the kids, and that's been nice. I still am glad he's their dad, but I am also glad he's not my husband.
