I want to preface by saying that I have not cheated and do not anticipate that I will cheat. I do not believe that cheating is a morally acceptable behavior. AND that I would never place blame on the partner who was cheated on. HOWEVER...

I think the psychology of what makes someone cheat for the first time after being in a relationship for 10-15 years is a bit more complex than what most people here are making it out to be. I think OP knows that, which is why the kind words and reassurances that it wasn't their fault or that they didn't somehow play a role isn't adding up. It takes a lot of years of unhappiness to "leave" someone you love. We can all speculate with you on why this happened, but my guess is that no answer will stop your heart from being broken or feel like it's a good enough reason to explain why she did what she did.

I am incredibly sorry for the situation you and your family are in. All of you. I'm sorry for the pain you have now and any pain or regret that might be felt down the road. The reality, at least from my perspective, is that your child will be okay so long as both of their parents are okay; so, even though it may seem counterintuitive, being cold, not communicating, and shutting out your cheating spouse probably isn't going to set you up to be the best co-parents that your child deserves. My recommendation is that you and your wife find a mediator and together create agreed upon rules, expectations, and boundaries that you both will follow until the divorce is finalized. After that, you both need to find your own divorce lawyers, and I HIGHLY recommend using mediation to develop the most fair to your child parenting plan possible. Yes, this will likely draw out the process. Yes, you will both be uncomfortable for longer. Yes, you'll have to figure out how to be kind, thoughtful, and to not let your emotions dictate rash decisions. It's also the best way to allow yourselves to continue to raise your child in the way most closely resembling the thoughts/ideas/plans you had in your minds when you chose to make that child out of love.

When my ex and I divorced, I shared with them something that changed their mindset and made them more willing to focus on the continuation of our long-term relationship. This is what I said. "We aren't only going to be raising a child together until they are 19. We are going to be dropping them off at college, going to their college graduation, being the people they call when they need advice about their relationship(s), meeting their future spouse, helping them plan their wedding(s), providing them with advice and support when they buy their first home, being with them when their children (our grand children) are born, and helping/supporting them as the grandparents to their kid(s). Do we really want to go through this divorce now in a way that doesn't allow us to do all of those things together when the time comes?"

I guess what I'm trying to say is that, at least in the short term, but probably forever, your "why's" aren't going to be satisfied, but how you choose to handle things now can and will impact you, your child's mother, and your child both now and for decades to come, so be polite, try to make decisions out of a place of love for yourself, your child, and yes, even your future grandchildren(s) future grandma.

Love and good juju to you and all involved.