I know you're going through a lot now, but be sure to take a good look what was going on in your marriage before all this. It sounds like she was checked out already. What would have contributed to that? Often the affair is a symptom of underlying problems. In no way is an affair justified, but often we see marriages which are just barely hanging together before the affairs starts.
An analogy might be if you were having money problems and she robbed a bank. In no way is that a justified response, but you should honestly look at yourself and see if you contributed to the money problems. If you're gambling and spending money frivolously while the rent goes unpaid, then you need to realize that you were part of the problem. That doesn't mean you caused her to rob a bank, but it may mean you contributed to the situation where she thought about robbing a bank.
Recovery is a long road, but doable. However, you *both* will need to take a hard look at yourselves to figure out what needs to change. Obviously she has the bulk of the work to do, but you should also strive to make the marriage one where she is happier.
And I don't mean to insinuate you were a bad husband or anything. It sounds like you're a great guy and she's lucky to have you. Hopefully she'll realize that and you can work it all out.
This is the kind of Bullhucky you need to put out of your brain and ignore for now.
This is the Reconciliation-Industrial-Complex psychobabble BS that makes people who were mistreated, betrayed, disrespected and exposed to life threatening diseases second-guess protecting themselves against people who are trying to use and manipulate them.
You may have been a crappy husband and lousy lover, but that does not mean that she did not have a hundred other options other than to screw some neighbor. She had agency and free will. she could have pursued MC or approached you about meeting her needs better. She could have divorced you straight up and walked away and let you pursue your own interests.
She had a million other options. She chose the one where she got it on and had thrills with the OM and came home with his semen in her exposing you to God knows what, while you were out working to support the family or home watching the kids.
It's this kind of crap that put marriage counselor's kids through college while BS's continue to get chumped.
Your job at this point is to protect your assets, resources and relationship with your children against someone who is cheating on you and preparing to divorce you. Your Job-1 is to get a lawyer and start preparing yourself.
If a year or so down the road after you are divorced and have your financial and child custody affairs worked out, if you want to sit on a mountain top and self-reflect and reevaluate your marriage, that is your prerogative to do so.
But at this point, this is just a bunch of background noise and Mind-Pollution that distracts you from taking care of Number One and protecting your assets and relationship with your children.
If anyone even suggests that you should spend time and brain energy evaluating your role in her wrapping her legs over some other guys shoulders, just turn off your ears and walk away and do what your lawyer says.