Listen, we're all glad you found SI, and I know it's tough to read some of the advice given. Especially when it goes against what you're wanting to hear.
At some point you're going to have to deal with this. You can stick your head in the sand and pretend like everything is ok ("because you love this woman" and "you want to have a family" with her). It's better to confront it now despite how painful it is.
Have you ever heard this phrase before, "you can't change what you're afraid to confront"?
I think RubixCubed nailed it when he said, "you are in love with who you thought she was, but she was NEVER that person".
Think about this, do you really want to be with someone, while married to you, said this to another man, "I think about you from morning to night and frequently dream about you" and "just so you know, I think about you in more ways than one...".
Your wife can try to spin this any which way she desires, but let's be honest here, she is flat out LYING to you when she says there was no sex.
Go back and read the messages you found (that you've posted here) and tell me she didn't have sex with this guy. There's a reason why the truth shall set you free, because lies keep you from dealing with the reality of a situation and until she's willing to come clean (and not just be a cheater but a liar as well) this whole situation and trying to rectify it is one big exercise in futility.
Chamomile is correct, being a parent is extremely difficult, and in order for it to work, there has to be enormous trust in the relationship and her claiming "she can't remember" doesn't just show she isn't trustworthy but she's also taking you to be a fool.
You are also correct saying that the bullet points you've listed are "insane"!!!
Picture this, it's early Sunday morning, you go into your kitchen to make yourself some coffee, and you look out on your patio to see your wife sitting there, deep in thought, smiling.
What thoughts are going to be running through your head based upon all these "insane" bullet point comments that you know about which let you into her mind about how much she loved this other man (while she was engaged and married to you)?
And when you called her out on it she didn't have the courage (nor any respect for you) to help you try to understand this MAJOR BETRAYAL, she, like a four yr old kid, obviously guilty as hell, looked you in the eyes and said "she can't remember".
I know you want this all to go away, and we all certainly understand how painful this. You think it hurts now? The only shot you have of achieving what you're seeking (a new relationship that's built on trust and hopefully to be blessed with children) is to deal with the truths of the situation. If your wife isn't willing to come clean and show that she really does want the same things as you and is willing to quit acting like a child by claiming she "can't remember" than why in the world would you want to be with this woman?
Saying you love her sounds good, but she is flat out showing you by her actions and her words that she not only doesn't love you but she takes you for a chump.
You get one shot at this thing called life. If you don't get the truth now, get ready for countless times ahead when you see your wife off in thought and it hits you like an eighteen wheeler wondering if she's thinking about this other guy.