What you found out about your wife and your friends should have no bearing on what or how you tell your kids. You're hurt and disgusted, but you don't need to burden your kids with that.
I think I kind of agree that you should have more certainty about how the divorce will affect them (where they'll be living, how much they'll be seeing each parent, what if anything will change with school, etc.) before you say anything to them. And I really think you and your wife need to talk to them together, with a unified story. I wouldn't tell them without your wife's concurrence.
It also sounds like you need to be upfront with your wife, at least that you feel the marriage is irretrievably broken and you want to divorce. Whether you let her know you found out about her "arrangement" is up to you, but I'd recommend thinking of the divorce as your escape route for you, not as a punishment for her.
Edited by TJMH (08/05/16 05:31 AM)