First off, it's not the greatest mistake of your life. You are 28 years old and only married for 4 years.

Secondly, you are not evil. You have needs that were not being met. Somehow, somewhere those needs were not being communicated to your wife in a way that had meaning and value to her. You were under the influence. It is not a scapegoat, but you cannot say you were completely sober in the act. So stop beating yourself up about it. But do not try to use that as an excuse to her. She is hurt, and needs understanding from you now.

She usually acts like it didn't happen, but when I bring it up to apologize and try to make things better she gets choked up and obviously is deeply hurt over what I did.

I'm going to have to agree with others here on this.. This is one of those moments that a Couples therapy session is needed. If she is not willing to discuss it with you one-on-one, then couples therapy is the best solution for this. Especially now that you both dont want to consider Divorce (even though it's not as bad as you might imagine) and you will always be a part of her life now that you are both parents of this new child.

I understand your situation. Alcohol has been a major culprit in the cause of many of our arguments as well.

She's hurt. thats all there is too it. You most likely cannot win her with gifts and multiple apologies daily. She doesnt want to re-visit it with you in conversation. I'm glad she loves you, because legally you've forced yourself onto her without her consent, like you said. That can be a very bad problem to have. However, you've said she loves you and wants to work it out with you.

That is why Therapy is probably a great idea now.

I hope you survive this. and when it gets tough, just try to keep a clear head. This is not as bad as you think. Getting therapy is your best bet, and continue to love her dearly. Good luck.