I'm so, so sorry you had to find this site. But you are welcome here. People who have been through similar situations are already weighing in and want what's best for you.
With that said, remember that YOU determine what's best for you--not your wife and not internet (or even IRL) friends who feel your pain.
Please understand that people are trying to give you their best advice, but you chose what to accept, what to think about, what to reject, and what to act upon. And that's okay.
Here is my 2 cents:
Many will weigh in urging you to take quick, decisive action.
You are still clearly reeling from the shock and horror--not only of your discoveries but of your wife's actions since your discovery and confrontation.
If you are shocked and hurt at her reaction and behavior (before and since your Dday), you're not wrong. It IS shocking and painful. The fact that she continues this inappropriate and hurtful relationship is beyond words.
If you are wondering how she could been in so deep so fast with this guy, it's the tremendous pull of feel-great brain chemistry from a new romance. Powerful stuff...and mostly fantasy.
You're the real dude who she shares real-life burdens and problems with. New dude doesn't carry this baggage.
Why doesn't she see the fact the the new and shiny will wear off ALL relationships? Why doesn't she get that all longterm relationships settle into reality and only get the new, exciting chemical dump once in while? Because she's super immature and incredibly self centered.
Being self centered is a prerequisite to cheating IMO. Self-centeredness is REQUIRED to make betrayal happen.
So, what are your next steps?
Some have said file for divorce.
Some have said boot her out too.
Some have said do a 180 and be ice cold. Grey rock.
Almost everyone here agrees that the "pick me" dance isn't working and won't work for you.
I say do what you need to do to heal YOU.
You cannot control her actions. You've seen that. You're living that, without question.
You can only control your actions. So, do what protects you from further harm and heals you.
Most here will urge you to avoid marriage counseling and opt for individual counseling instead. You need to heal and protect yourself. And, if she is willing to do counseling, she has a LOT of work to do on herself. She isn't acting like a good candidate for marriage counseling or for any kind of reconciliation at all at this point. She would need to truly go no contact with the affair partner, show true remorse, take action to work in herself, and be transparent in her actions, whereabouts, and communication in order to earn a chance at reconciliation with you. You're not seeing any of those actions. You're seeing the opposite.
You didn't deserve this. You don't deserve this. Believe that.
Care for yourself.
Give yourself some time and space to begin healing and to make decisions.
Again, just my 2 cents.
Sending support your way, Owl!!