Good for you that you are trying to get help! It's already a big step.
I know you have answered lots of questions already but I couldn't understand weather you felt abandoned before the second child or if this situation was happening before.
My point is that besides of what everybody else already stressed about ending the affair and showing remorse one very important thing for you to rebuild her trust is to understand why you truly did it.
I understand your point of feeling abandoned. What I can tell you from my experience is that my husband had his mess when I was going through a very hard time in my life. Despite that he tried to compensate in other ways just like you did for your wife, I felt abandoned when I found out that the support he was giving me was not complete since he had to deposit part of his emotions outside the marriage. It was not because I was broken that I wasn't in this marriage anymore. I do not want to judge you but try to see it with other eyes. She was having issues with the pregnancy, I cannot tell for sure but you probably did not look for outside counseling to figure her issues out so she was trying to solve them for herself along with her needs. Nevertheless she did not cheat on you.
Anyway, what I am trying to say is that a bad marriage even with no affair in the picture, is a consequence not the cause. Probably you will have a better chance if you understand what was the cause.One mistake does not justify another. It can explain but not justify.
