Morning OP. Don't think of him as helping you, but of helping the children. I too would hate having to rely on him. And remember, they're his dc just as much as yours, so he's not helping out, he's fulfilling his responsibilities as a parent. Bear this is mind when he starts expecting you to thank him. You don't have to. He should be thanking you for letting him back in to be with them.
Stay in bed, sleep if you can, get well. If you're up to it think about how you're going to get things sorted for your life without this cheating, lying man in it. Number one, smile at the fact that you will be better off without him. Better you know now what he is.
Disengage. Don't share any plans with him. Don't get involved in anything other than practicalities and matters concerning the dc.
A man who tells you he had an affair because you weren't doing the right things/making him happy enough etc is a snake. Justifying himself in this way is unforgiveable, it's so low. If he's found his soul mate, good, he can sod off and cheat on her. If they are matching souls then god help them, two cheating, selfish liars. So yes, a good match.
Try not to show him you're upset. As you say, you need to move to a point where you are indifferent to him. Unfortunately you have to go through all the other stages first; grief, anger, sadness etc. But you will get through. You are in the right, and this will give you strength.