I am still living in the dream world that one day he will actually feel the pain of his actions and want to be a better person.
You know, if he was a previously good guy who just slipped and succumbed to the allure of an affair - this would be possible, even likely.
But we've already established that your H is a serial adulterer and liar - he lied to you about cheating on his first wife to be with you. He engaged in an affair while you were pregnant with his child. And now that he's back, he's wanting to sleep with you but still telling you he's in love with the OW.
Odds are pretty darned good that he has a personality disorder and is unlikely to change. If you "win" him back, you will always be looking over your shoulder, waiting for the next affair to happen (and it will).
Is it possible for him to change? Sure, change is always possible. Is it likely? No. And if it DOES happen, it sure won't happen because you let him stay around the house and slide back into your bed. He's only going to change when he HAS to - like, when he's lost his wife and kids and has to face up to the effect it's having on his life. Right now he's protected from all those effects.
Now - if you need him there for help, and have ABSOLUTELY no one else who can help you - fine, use him for that right now. But don't be deluded into taking him back without him doing all the hard work he needs to do - you'll regret it. And you deserve better.
