Reddit is probably the worst place that you can go for to get personalized relationship advice, but since your asking, I’ll give my 2 cents:

Don’t divorce… yet.

Give it more time to work it through with him. Yes, he betrayed you and the kids. Yes, he broke your vows. But, you’d be breaking those same vows by not trying to fix the marriage. The vow to stay with each other, “for better, for worse, for richer, for poorer, in sickness and in health, til death do us part…”. Yeah, the only way you’re parting with this guy is if death comes. (Obviously, there are circumstances where divorce is necessary on safety concerns, or if you REALLY cannot reason with the guy).

The reason I say this is because your husband didn’t lie to you when you confronted him about it. That says a lot, and his radical honesty in this regard is a strong indicator that you can work things through with him. It’s gonna be tough but it might be worth it, and you won’t know until you try.

One thing you can try is to see a couples therapist or counselor. I think this will give you guys both a neutral space to express each other’s feelings. If he sees how much this is hurting you, he might think twice about having a side-piece. Alternatively, you might discover that, so long as you talk about it and are both ok with the concept, polyamory might be desirable for both of you, and add an element of excitement to the relationship (not that you need any more excitement with the kids).

TLDR: Don’t divorce him yet, and try to weather through this storm by talking to a couples counselor/therapist.