Here is the very first thing you need to get very clear in your head:
Your wife may have very legitimate gripes and resentments from your marriage.
You probably had some as well.
She, for reasons of her own, decided that rather than talk to you, demand counseling, or ask for a separation (a reasonable escalation) she would have an affair with someone else. Between the length of time, the repeated going behind your back even after it was out in the open and the DNA test - I feel fairly certain you still don’t have the full picture. I seriously doubt this was just an emotional affair.
So her unhappiness with your behavior is not an excuse for her actions. It was a legitimate reason to do all the things I listed above - and even up to divorce, but going behind your back to get a child with another man? That would be a huge breach of trust without the affair. It is the most personal choice a couple can make together!
Then to have an affair with the guy for months, even years, right under the noses of your and his wife? That is SERIOUS DUPLICITY.
The fact that she has the nerve to be angry with YOU and blame YOU for it does not speak well for her character or desire to change. If she isn’t taking the initiative to save your marriage, you shouldn’t put your energies there either. If she does, you can meet her part of the way, but saving this marriage isn’t one person’s job. It’s for two people - and she should take the lead.
As Keep said above - no one EVER wins the “pick-me” dance.
Insteadof chasing her, take some time and emotional distance and make sure you REALLY want the woman in front of you. Sometimes we fight for something because we don’t want to lose, not because we want what is there. This is a time to be very, very clear on your own motives.
if you realize you don’t - leave.
If you decide you do - consider reading about, and acting on the 180. Not to get her to choose you, but to see if there is any hope for the relationship. Because if she doesn’t react to you pulling away, then her heart has already left the marriage entirely, and you are fighting a losing and demeaning battle.
So sorry you are going through this. We all understand this pain.