If the reason for your divorce was because of infidelity, would there ever be justification in telling that to your children?

I believe that my wife if cheating on me. I don’t have any proof (yet) but all the signs point to yes. Late nights out with no explanation, saying she has to work but not there when I call, etc. We have been struggling with marital issues for some time now and I’m moving closer to making the move of divorce. I know that if she is cheating, all bets are off, this marriage is done. The kids are in a tough spot. I would like to preserve the marriage, but not at that cost, and part of me would want them to know the truth. But that’s just wrong, right?