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.
M: 40 H: 44 Married 14 years S11 & D6; D20 & D19 from previous M 2BDs/PAs, 8 years apart Piecing: April 2014