You have nothing to be ashamed about.
In my opinion, you are being far too nice in the separation process. She screwed around, but she stays in the house?! Unless you have legally handed it over to her, go back!!
She repeatedly stabbed you in the back - you do not get a special medal for being nice. Don't get me wrong, starting a war would be stupid, but at least start fighting for yourself and get the best deal for YOU.
Furthermore, you leaving the marital home could have major implications on custody of your child as your wife could claim abandonment. If you decide to leave after, then no problem in leaving.
The following is what I would if I were in your position;
1) March straight back into the house if you are still legally able to. If she resists, just say that you have every right to live in it as she does.
2) [Optional] --> Grab the marital bed and throw it out symbolizing her destruction of the marriage. I know of someone who actually set fire to it in his backyard. Yeah it was a bit extreme, but also incredibly cathartic.
3) Employ 180.
4) Get a lawyer and file for divorce. Get the best deal for YOU. Not her, YOU!!
5) Expose her to families and friends through a cold email. Something like: "Due to my wife's relationship with a 3rd party i have decided to file for divorce. The purpose of this email is not to shame my wife, but to inform people the reason for our separation as well declaring that I intend to remain a big part of my son's life. I am fully committed to his upbringing." Something like that - do not get emotional and start blaming her etc.
6) If the other man has a girlfriend or wife - expose to them as well.
If this man is a player/predator you could put him up on cheaterville..com. Again this is not out of revenge, but to warn other people that this selfish man has no problem destroying people's lives for sex. I would put him up regardless and link his post to his work and family. This man had absolutely no problem wrecking your life.
My thoughts are with you.