Always utilize self-preservation.
However, that does not mean you cover up her nasty little secrets.
You don't ahve to order a banner to fly over your town announcing "Mrs. PJ is an adulteress/homewrecking a--hole!" (though it does sound funny) but...
when people ask, tell them. Straight up.
People: Well what happened taht yu're getting divorced?
You: Mrs. PJ is currently involved in an adulterous affair with a married man and has decided to pursue that.
Be matter of fact. You don't have to cover for her. She chose this, remember?
If he's married and his wife doesn't know, tell her today. She has a right to know.
I thought you said your wife filed already? if so, get a la\wyer and respond. If she hasn't, serve her with D papers fast. Then be stealth.
Then only speak to her about the kiddos. If the kids ask what's going on, tell them the truth: Mom has a boyfriend and has decided to pursue that. End quote. Don't go into details. Mom can explain. This is her doing.
Be cool, be confident, be collected. Stay above the fray.
You have nothing to be embarassed about. Be the best dad for your kids.
The more together you seem, the more it's going to piss her off. Guaranteed.
So be your calm, cool, bad ass self, the one she first met. Only now act like you're not into her.