I haven't followed your sitch enough to chime in with confidence, Dad. And I know I'm likely in a minority here (bc it does tend to go against DB principles), but why NOT mention the OP to your children? Sure, take 50% of the blame for the breakdown of your M. But I would NEVER - ESPECIALLY in front of my children - accept 50% of the blame for a D that is happening because of an A. I wouldn't accept even 1% of the blame for that.
Yeah, it may seem like talking openly about the A will stand in the way of reconciliation. (In my case, it didn't.) What it DID do was show my kids that if they were going to live in a broken home, it wouldn't be because that had been MY choice. No, it was not motivated by self-righteousness; it was motivated by truth and my desire to show my kids I was willing to fight for our family. Even in the face of an A.
Regardless of what you choose to do, I'd urge you to demonstrate some self-respect. No one likes to see a man being a doormat.
This ^^^. Do NOT lie to your children; it's imperative that they know that as their family goes thru this sad change, at least ONE of their parents will always tell them the truth.
Your wife should tell them, and you should chime in as needed if she tries to lie.