If you take him back, this is what will be going through his head:
Phew. Got away with it. She's basically given me the ok to do it again because for her, anything's better than splitting up. Kept the house, the cash, the kids.
And next time I'll be more careful. Super careful about covering my tracks, always on my guard about letting anything slip.
And there will be a next time. Because I've got a habit now. The nice cosy socially approved image-boosting set up of being a family man.
Plus the experience of an exciting, energising bit on the side, and how to get it.
And right now … I'm one down. I've lost out on the naughty bit. I'll be looking around for the next candidate for that bit of my life that I'm probably never going to forget I once had and already miss.
Because you made me give it up.
—---
I'd like to bet the OW's husband didn't know. Because when men find out, all hell breaks out. DH would probably have a black eye by now, and depending on his character, so perhaps might she.
I'd also bet his time to himself was not spent dumping her, it was trying to persuade her to dump her DH. And she did the weighing up and said no.
So here you are, second best. The consolation prize. Can't have what he chased, so he'll settle for what he's got. Do you really want that?
Also, you will never ever forget. It will sit there, like a toad on a birthday cake, ruining everything nice. Knowing he cannot be trusted. You'll be on edge forever, checking for lipstick on his collar, mentionitis, odd phone behaviour, changes in manner, dress, interests - everything will become a what if …? Paranoia, suspicion and angst. Every argument it will be brought up again, just below the surface. If he is still working with her, you'll be eaten up wondering what they're talking about right now.
And the apologies, promises, I'll do betters? They're an act. A mask created to deceive and deflect.
Only you can make your choice. But it must be an eyes open reality based understanding of what the future will be like for you and your children if you take him back.