Hello Friend.
First, welcome to the best club no one ever wants to join.
I'm very sorry you're here. It's always a sad thing to learn the one you've trusted with everything has betrayed you. It makes no sense. Affairs never do. There may have been issues but an affair is not the answer. It only compounds.
This is not your fault...at all. I don't care if you were the worst husband, which you probably weren't. She had no right or excuse to do what she did. Understand and accept that first.
Now, what to do. I'd see a lawyer in order to know my rights. I'm not saying file for divorce, but you want to know what that would look like in case that becomes an option in the future. Also, you've experienced a trauma as severe as a physical attack or major accident. It may help to speak with a couselor or clergyman if you are religious. DO NOT do marriage counseling yet. Maybe down the line, but right now you wife is not ready.
Right now, she is in save-her-a$$ mode. She wants to rug-sweep, get back to normal and for you to move on and get over it, as if all she did was break wind. That NEVER works. Either the affair will go underground or rekindle later or she may have another affair with someome else, figuring she did it before so no big deal. Right now you can't trust anything she says or does.
If you want to stay together, do not offer her that second chance for free. She has exausted any credit she had and must EARN everything back. You'll get lots of good advice from the veterans here. Take it or at least what would work for you. It will often be painful so brace yourself. Complete honesty, a time-line of the affair...with details: who, what, when, where, frequency of meetings, places, collaborators (her girlfriends and/or co-workers for example) and even specific sex acts if you think you can handle it. I say this because you'll probably imagine worse than what was going on.
Complete transparency if you want it. It's a pain to have to check up on a grown person, but this act brings home the magnitude of what she's done.
Consider a lie detector test. Very effective at getting any details she's 'forgotten' about. There are many cases of parking lot confessions here on SI.
Exposure...to family, friends, her job if it's with a co-worker, the kids and especially AP's wife. People tend to take sides and her family will tend to support her, but the knowledge and embarrassment she'll face will help snap her into reality.
Most importantly, take care of yourself. Give yourself time. This will be a marathon, not a sprint. It takes typically 2-5 years to get though something like this no matter the outcome.
Sorry for the novella. Good luck.