What an absolute C * N T. I am fuming for you.
What was your relationship like? He will probably blame you.
I know on here ppl are inclined not to fault the OW, usually the onus is all the DH, however, what a witch she is, she knows your whole situation. I think women in these instances get off from knowing that a "taken" man is so enamoured by them, that they risk their tearing their family apart to get in their knickers. It is an ego boost. When really, they are getting the booby prize, running off into "the sunset" with a cheating, disloyal, lying son of a b*tch who will one day do it to her too or worse. What is so attractive about a man with no integrity? I just don't get it. Women should run from a man like this, not aim to win him like he is some prize.
OP... he deserves to have his ass handed to him. Be smart about this. Great he is a good father, let him know the door will always be open for hi m to parent your daughter and always facilitate co parenting, however, because of how badly he has betrayed you, you need to CUT HIM OFF from you completely. You shouldn't even be willing to discus the matter. Just demand that he leave for a minimum of 1 week until you can decide what's right and get your head straight. But for your sake, do not let him work his way out. Sadly it sounds like he wants out anyways, he wanted you to see those messages, and he is no longer engaged in your relationship. As such, open the doors very wide for him to get the hell out, and don't look back, not even a glimpse.
He is not he man you think you were going to marry. The universe has saved you from who he really is. Be grateful.