I vehemently disagree with this. No woman or man should stay in an abusive relationship "for the children". And unremorseful infidelity is indeed abuse. Kids always know what's going on, or at least that something is wrong, and it sends the wrong message and teaches them the wrong lessons to stay in an abusive marriage and allow them to form that impression as the "norm".
If anything, you would leave the marriage for the children.
Staying in an abusive relationship implies ongoing behavior. If so, I would agree with you. But I was under the impression that we are talking about a single instance.
It's never black and white. It's not abuse, it's dishonesty. There is a difference. While the cheater is the guilty party, it's pretty rare that both parties don't share at least part of the blame.
Kids who are old enough can also learn that even big mistakes can be forgiven if the person who made the mistake is willing to change themselves.
The key is to truly look at what is best for the kids. Sometimes that means staying together, and sometimes it means getting out. And those circumstances change over time, so you have to constantly assess the impact on the kids and make the hard decisions when appropriate.