ok, first of all, I think you need to be very honest with yourself about what your goals are for you and for your relationship. Think about who you are, were, and want to be and start making some positive changes to you, taking into consideration the feedback your wife gave you in her email. Someone somewhere on here posted that they told their WAS they were attempting to be better at handling rejection and said, I'm going to ask you to do things, feel free to say "No", my therapist suggested that i work on this. Do you need to get better at handling criticism? It could be positive for you in this situation to say, I'm responsible for how I acted, W was being supportive and maybe I was defensive. Can you help me work on that by being very honest with me about how you feel about what I am doing? It will be hard for me to hear sometimes, but I'd like to be a good father to our child and I appreciate your ability to help make that happen with honest feedback. But, I would also like you to tell me when I do things well, not just when something is bad, so I know to keep doing it.
Just an initial thought - it has to be you saying, maybe I slacked off and that's not who I want to be as a person.
So, on the other hand, that doesn't erase her contributions to this situation, or the terrible way she betrayed your family. You were willing to make it a "freebie", but she's clearly not ok with that - maybe neither of you are really ready to deal with these feelings and this part of it. And maybe the numbness you feel is you finally starting to feel like she's really sorry and that lets some hurt in. The thing with DB'ing is you delay dealing with some of these emotions because you get so set on your goal and your life. Be careful that as she opens up to you, that you don't unleash the floodgates yet.
This is classic female "here's a roadmap, but it's written in code. I don't think you'll figure it out, so I'm going to make it hard and unclear so I won't be as disappointed when you don't."
She's uncomfortable around you and thinks you are too. Find happy things to do. Can you take your child to the zoo? Can you do things together that are relaxed, not relationship related, and fun/that put you in a good mental space together? She's opened a door to that time together - don't ignore that or over do it. "I drove by a new playground that I want to take D to. Would you like to go with us?" If you're together, go with something that allows a nonpersonal follow up - "I saw this article/movie/comic strip and thought you might enjoy it, I'll email it to you" Think about what she loved about the you she fell in love with.
Also, keep a eye an out for ways to show her you are not just thinking of her as an object on your arm. Tell your child she's got a great laugh/heart/commonsense/sense of humor/brain, etc and she gets it from her mother. Appeal to her intelligence, sense of humor, loyalty to her family (including you, in spit eof the cheating).
Be patient - it's going to take awhile for you to make these changes in yourself and grow from this. And she won't fall for halfway - don't let her. The more this costs you both, the more sacred you'll keep your future relationship.
There's my book of a reply - let me know what you think helps/doesnt really apply to you. Everyone is a little different. I see that email as a potential positive - my H won't say he's sorry. He's too wrapped up in his own guilt and depression to deal with what he feels about me.
Faith is, at one and the same time, absolutely necessary and altogether impossible. --Stanislaw Lem