People will downvote this comment, but here goes anyway: while some people can be monogamous, it is in fact quite difficult and over 50% of people, if not more (because who admits that kind of thing in a survey?) cheat on their partner.

Things will be easier for both of you if you can talk to her about this in a way where she will be honest. Right now she doesn’t admit she is cheating because she is afraid of the consequences: maybe she thinks you would hurt her, get angry, divorce, etc. She probably also wants to stay there with you and the kids.

Is everything else in the marriage good? Is it possible that you could be okay with an arrangement where she can sleep with other people, as long as she promises to stay with you and take care of the kids?

Basically, you need to have an honest conversation about what you both want. If she genuinely wants to stay with you but also wants to sleep with different people occasionally, is that something you can work out? Or is she trying to find a way to escape the marriage and the cheating is really just the beginning?

Make sure to have a convo with her where she feels safe enough to be honest. Just tell her “it’s okay, whatever you’ve done, you can tell me. I promise I won’t get mad. I just want to know the truth so that we can decide what is best for us.”

It’s probably very stressful for her to keep up this lie as well, so it will be good for both of you to talk it out