I am wondering what happened 2 years ago, how you got through it and decided to go on. Counseling? Ignoring the elephant in the room? Something else? I would go back to that, but I bet there is plenty from that time that is thoroughly unresolved and unexplored.
And, if he was so over you for 2 years, why did he father a child with you, and relatively recently, for that matter?
Essentially, his story stinks, it doesn't hold up.
I vote that he was looking for some variety and, once he got caught, is trying to deflect the blame onto you. Regardless of what happened 2 years ago, he is a big boy, and he is responsible for his actions. Not just his actions in terms of making calls and signing up for a dating site, but also for creating a child with you.
I recommend counseling, mainly because I think you would like to at least make an effort to save your marriage. But I am not terribly optimistic, sorry. I do think, though, that when it is a marriage and, particularly, when there are young children involved, that couples should make big efforts to try to save what they've got. But that does not mean that, if all signs point to ending it, that that cannot happen.
Best of luck to both of you.