Try sitting in the same room with your cheating H watching a movie because you want the kids to be with him, but they dont' want to be alone with him yet (or maybe just want me near so I don't "disappear"--who knows). Popping popcorn and baking cookies. This is because he has no place to entertain them himself. So I welcome him into our home. I am a flipping saint!
Tig,
This is a hard row to hoe. I did this for years. My H didn't cheat, but circumstances were such that I did this to facilitate his visiting D's. Was it right? I will never know. I do know it was hard on me.
I don't know that you are a softie. I think you see a bigger picture.