Some opinions as someone who has been on the other side of this:

1. Recognize that if she decides to not divorce you, from now on, no matter what you do, how much of a new leaf you turn, etc., there will always be at least a little bit of doubt about you. That feeling when you find out you've been cheated on by a long-term partner never quite goes away - it gets smaller and less nagging, but never completely disappears. If you want to stay with your wife, you're gonna have to accept this.

My discovery happened almost a decade ago. I would have been well within my rights to dump her ass and never talk to her again, but I didn't. I thought it was at least worth trying to stick around and see if we could work things out before doing that, given we made that whole "till death do we part" oath and were still breathing. She was not owed this - I did that for me. Things are better, and we are in a much, much better place than we were. Still, this pops to mind at least once a day, and has every day since it happened.

2. Go see a couple's therapist yesterday - first, to create a venue where she can express her feelings about all of this, what she wants to do, and what she needs; next to start having an open, 100% honest discussion about where your head is at and behaviours, and finally to start shopping tools for completely transparent communication going forward. Treat this seriously and pay fucking close attention.

3. Follow this up with some therapy for yourself - very few people choose to cheat because they're loving life. Start identifying where you need to work your own shit out. Again, take this deadly seriously. Encourage her to do the same.

4. 100%, no exceptions, complete and utter honesty and transparency going forward. She wants to see your phone? Hand it over. She wants to know where you're going/what you're doing? Tell her, with proof. She wants you to have a tracking app? You download that shit. She wants the nastiest details about what the hell happened? Do warn her you're concerned it will hurt even more, but if she wants to hear it anyway you tell her. By dint of your actions, you've lost your right to both be in the relationship and keep a self-defined level of privacy - if you don't like it, start looking at divorce. If you two start healing, the need for this kind if stuff may start to diminish as the level of trust comes back up.

5. Check in with her, often. How she's feeling, what she needs, etc. Pay attention, respect it even if it involves something that may hurt you emotionally. Do NOT throw shit in her face - keep in mind, YOU'RE the one who fucked up, and who now wants to move on with her as your partner. She just discovered her husband did one of the shittiest things a spouse can do to someone they claim to love. It's a very different experience.

6. You could do everything right, do all the therapy, open communication, working on yourself and the relationship you want. If she decides that she can't do it, she can't. Recognize this. Accept this. She doesn't owe you shit.

Not gonna lie to you man - you have a tough row to hoe. I will say, with time and a shit ton of work, it's possible to remain together, and both of you be happy about it. But there will now always be a pre-cheating and post-cheating division when thinking about your marriage. The goal, if you are remaining together, is to build something much better and stronger than what you had before. That may happen, that may not. But putting the work in gives the greatest probability of success.

Best of luck to you - seriously, you fucked up, and fucked up BIG, but we are all human, and therefore liable to fuck up. No matter what the outcome of all this is, learn from it and grow.