Even if he didn't cheat with you before they split up, you were absolutely mad to start seeing him one month out of an 11 year relationship when he had a 3 month old baby at home.
Many family break ups aren't clean splits where they decide to break up and that's it done. There's often a lot of feelings left, they still feel like they're together in lots of ways even if they said they weren't in words.
You said he saw his kids every day, so presumably that means he's in the family home every day and not taking the kids overnight, all reinforcing that they're still a family. Very very easy for them to slip back into bed together and he won't feel bad about it because his history and family is with her.
But you did cheat so there's even less reason to expect any loyalty from him. If he can cheat on his partner who has a small baby then he can cheat on anyone.
And now even though he cheated on her and was lucky that they managed to be friendly afterwards he then goes and sleeps with her even though he doesn't want to be with her? He really doesn't care about peoples feelings does he?
I would say there's a high chance he hasn't told her that they split at all, and she just thinks they're taking a break and working on things.
That's if he still isn't living in the family home!