I feel sorry for your retarded mind
David we know you are hurt and currently ongoing through a traumatic experience, that's why your offense is tolerated one time here, especially if you did nothing to in particular warrant the cheating.
But be careful how you talk to HPS and others during that state, everyone wants to help you. What HPS describes here is that if your marriage has been failing, it generally happens from two sides. But you shouldn't take the blame here as what they did was in their own accord.
She could do it first or you could do it (theoretically). Generally the way of the punishment cannot be judged on sheer emotion but on the level of the offense.
What you particularly described is a high level of offense. Regardless on if you walk away you have to examine how you treated your partner, however in my experience, some people tend to do these things no matter how they have been treated.
The "reasons" she gave you are totally retarded and it's best to leave her and move on with life. As there are no children involved and not heavy lawyer fees involved, then just walking your way should be sufficient.
Without children there is not even a need to "get evidence" to show to nobody. Since nothing ties you together besides a very simple and weak relationship which has been fully violated, there is not much to look into here.
Counselors can help in many cases, but you will feel mad at yourself and hate yourself if you find out this happens after 3 months again. Many people do not take that counseling seriously In order to take it seriously, serious respect must exist and it must have been a serious lapse.
From what you write a serious person wouldn't respond to you about your dick or something, she thinks she is a teenage adult and learning about her genitilia still during what you consider your marriage. Better to let go.
The only thing to make you stay would be if you don't care at all, like zero, or if there were other serious things that matter more than this. Yet this type of life has to be done upon a mutual agreement, which was clearly not the case.
Therefore what remains is just damage to you as a person. Might as well leave.