Hi there Brly:
I've never posted on this forum after lurking for quite a while but your story resonates with me - sorry this is so long. The differences for me was the kids were older (14 and 16) and it was MULTIPLE affairs. But I thought I'd share what I did after I read her email and discovered what was going on.
First of all, take care of yourself - go to a doc and get something if you're not sleeping, eating etc. Get tested for STDs. Take care of your kids - you decide whether you want to tell them what going on, not her. I decided to not tell my kids pending the results of the critical meeting below, and ended up not telling them at all.
Go see a lawyer. Find out what the score is. For example, in my Province, it's a no-fault divorce, trying to get a divorce based on adultery is really difficult and expensive, so best to separate for 1 year, split assets and file paperwork through a service for $500. Spend some time planning how to exit, making preparations, and getting a script together for one more critical meeting with your WW. Get a Voice Activated Recorder and keep it on you to record interactions so she can't claim you abused her. Get a GPS tracker for her car. If legal in your country of course.
On the critical day, I disclosed the affairs(s) to the spouses of the APs via phone. I sent them PDFs of the evidence via email. In one case the marriage exploded, locks changed, accounts drained, screaming matches in the driveway in front of the kids, the whole 9 yards. Very satisfying. In the other case, rug sweeping because the AP had cancer etc. (which was very satisfying as well I have to admit). My WW's phone blew up obviously as her APs freaked out at her. I didn't call anyone else pending the results of the day.
When she got home I said nothing, went about my normal evening fixing the kids dinner, etc. My parents were poised to remove the kids from the scene if I called them, but I just put them to bed. We went for our usual evening walk, then as we walked up the driveway I said "We need to talk." She was sh*tting herself by that time.
The critical conversation was: "I know about the affairs. I know a lot about <name> and <name> and <important affair occurrences>. As I see it we have two choices. One, you decide to stop this garbage immediately, start acting like a married lady, work your a** off to make amends, make me feel safe, and maybe we can recover some semblance of a new marriage. Or if you want to act like a single lady, you pack your bags and get out, we sell the house, separate our assets, and you'll be alone. Time to choose, let me know." And I waited. She knew I was deadly serious, and that I would make her life a living he** if she chose option B, given I'd already outed her to the APs BWs. I knew being outed to her kids, family, friends, coworkers etc. was her worst nightmare.
In my case she immediately caved, handed me her phone, and passwords for all accounts, and sent no-contact emails (written by me) to her APs, with me watching. I made it clear this was the last chance to come clean, and she did. Over the next few weeks and months, she started working hard to make me feel safe, let me know where she was, came right home from work, refused to go shopping etc. without me, and generally worked her a** off to try to make things work. When she got her phone back (with a new number) she immediately turned on the Find My WW (as I call it) function. Her car had a GPS tracker in it as well, in case she ditched her phone. Seven years later she's still trying, although she's not as diligent as she was at first. On my part, I'm not the fidelity police. She strays again and we go right back to the beginning with option A off the table. In the meantime our financial situation is better, kids are adults, and Hysterical Bonding was pretty fun. I have a hair trigger to cut her loose these days - with retirement on the horizon it may end up being the last straw if she isn't interested in spending our retirement doing something we can both enjoy. She says she wants to keep working, which to me is a deal breaker.
So in your case, she needs to know you're not fooling around. The affair needs to be over, and you can help kill it by turning the heat up. I know she's disclosed to her mom at least, but be prepared to disclose more widely. On a critical day, a few calls disclosing the affair, or asking people for support in saving your marriage would mean she's under immediate heat and facing consequences. It shows her what "single lady" life looks like. Try hard to make her understand what that life would be like.
You choose as to whether you're willing to try to rebuild and reconcile. It's hard. It's years of eating a turd sandwich and not really feeling like justice has been served. However, there's absolutely nothing wrong, to me, about not wanting to blow your life up for something she's done, but you're getting good advice here, so follow your own path. But you really need to draw a hard line, and make it stick. You may be surprised - my WW told the APs she loved them too. She didn't. She loved the thrill of doing something illicit in her boring life. But she loves her house, her kids, and her life (which you're an integral part of) more.
I hope this helps. Best of luck, and really sorry you're here.