Don't be with someone who cheats - what's to stop them from cheating on you later?

And, if I'm not mistaken, that's exactly why you guys broke up in the first place!

You deserve better. I'd also consider that the other women is a stepmother to your kids, and even if the two of you got back together & she was shunted away, how would your kids react to that? Do they like her?

She doesn't deserve that, either, to be frank.

But more importantly: he's using you & you need someone who isn't going to cheat on you.

I would talk to him and explain that you won't tell his wife should he decide to not be with you, and then push for honesty: with zero consequences and a chance to be 100% honest, most people will take it; if you try it, he might choose you over her or he might take the opportunity to end things.

Be prepared for both.

Another option would be to simply tell him you can't keep it up; which might be a better solution, depending on what you choose to do.

Good luck! :-)