Welcome to the forum! Glad you found us, it's a great place for wisdom and support.
You aren't married, the kids are not his - this is a plus as far as breaking it permanently. Oh, and he has admittedly cheated on you, refuses to see he has a problem, refuses to consider your feelings. Sounds like he's made his choices, and yours, for you.
He likes this other woman because she isn't an impediment to his lifestyle, until she also sees the light. You and the kiddos are the main focus right now.
Sorry I don;t have much more to offer up at this time. I think you are pretty clear-headed if you've already left.
COD