Gordie - to answer your question, my h has never been open about OW. In fact, I don't know for sure if he's had affairs. Mine does seem to be a bit of an outlier. Of course, in the early madness of this, he announced he was going to sleep around and then come home to sleep/eat here. I said no. He seemed surprised. So he may have buried his double life given this.
As for you having to be the bad cop w/your kids, embrace it. I too was cast in this role for a long while. Kids feels safer with rules and boundaries. They may fight you but deep down they respect that. Months ago, when my niece came to visit, when my kids were alone with her, they told her that I had my act together and that I was on top of their lives. I was surprised by this because we were butting heads a lot. My h was a mess and I was re-directing their lives. It strengthened my bond with them. (I showed tons of affection too--tousled hair, gave hugs, listened, etc. But I never let them use their messed up dad as an excuse to do poorly in school or get away with things.)
The kids do watch and they know who is on their A game. Proudly differentiate yourself from her and . . . fast. They will remember the safe zone you created.
Me 41, H 47, M 15 yrs, S11, S13 BD 1: 11/4/14 we work on it; really I pretzel myself BD 2: 3/31/15 H goes down to "dorm room" 8/15: H back to MBR 10/15: H back in dorm room 1/18: H files, now divorced