Infidelity Support Group
Any relationship in which one partner engages willfully in sexual relations with another outside of the partnership is considered to have experienced infidelity. This breach of trust is often traumatizing for the faithful partner as well as the relationship, and support is often needed to heal emotionally and to decide whether or not the relationship should continue after...

As for what we told our kids, we used the same reasoning and judgment as when we talked about violence, sex, religion, politics, or any other sensitive subject. We gave them only the basics in an age-appropriate way and then answered their questions honestly and directly if they had any. If they didn't want to talk about it, we didn't push the issue. I was careful not to tear down my husband's character (or the OW's), but rather just share facts.
Kids can tell when something is up, and they'll use their imagination to fill in the blanks, so it's best to fill them in for them. Fear and anxiety can create filled-in stories that are much worse than the truth. Again, ugly things grow in the dark.
Now... all that said: there are absolutely reasons NOT to expose an affair - especially if it jeopardizes the health and wellness of anyone involved - including kids. There should also be a logical, calm, and mutually agreed upon exposure. One partner crap-talking the other isn't the way to do it.
For more on exposure, I'd encourage you to check out Dr. Harley's thoughts on the matter: https://www.marriagebuilders.com/when-should-an-affair-be-exposed.htm