You hit something for me - I've stayed out of this mostly because I wasn't sure, but for those of us with kids, you are exactly right.
I tell my kids divorce is wrong. I tell them adultery/affairs are wrong, and I explain to them why. I tell them that I love Mommy very much, and I am committed to her, and I would never be with anyone else.
I am their rock. I am their stability, their consistency. I have kept them in their home, W moved out. I have kept them in their church, their school, their normal habits.
W has spent most of her time with OM, and the kids are very conflicted and confused about it.
If I pick up OW - they will lose their rock and their example of how to treat a spouse, and how to love your spouse. They see me respond to her anger with kindness, and they see me spend time ONLY with them.
Dating would just blow them away... They can't discern what a "friend" date is - that's what Mommy told them OM was at first, then she lied about it.