You need to get firm and have contact at his house, because you're separated. You need to have him come and pick up the DC and take them back to his place.
Then when he brings them back, he leaves.
You're using the DC getting upset as an excuse to continue this unhealthy pattern. Stop doing that and they will adjust in the way that other children from separated families do.
What was the agreement when you split up? That you could see other people?
It's not a situation I could handle, but I'm not sure it was exactly an affair scenario either. It's a shame smother life was created so thoughtlessly.
Do you believe you have the truth about this? That he only met her during the separation?
Anyway, to stop yourself feeling crap after sex with him, you have to change things.... Or decide if you can make it work and get a plan together to reconcile.
A lot of trust has gone, because you found out about the baby so late. He doesn't sound trustworthy TBH and she will always be in his life because of the baby.
If she met him genuinely thinking he was single, then it's not good that he's not involved with the child in any way, however, I do wonder about women who have a child with a man they hardly know. Craziness.
A million people will say it takes two... Off course it does, but I personally feel that the woman should be more responsible, because having a baby has the most impact on her and as is evident, a man can just swan off.