Life choices are often about perspective. You have painted it as you walking out on her, or you separating or splitting up the family. It doesn't have to be that. It can be breathing room, growing up space, and a time out.
Are you really looking at what staying means?
You have a completely unremorseful wife who thinks all of this is your fault.
She has flaunted her affair to you and her children. She took her children to associate with this man and had them stride around in clothes he bought them. My H hasn't even done that.
What will your kids think of your decision to do nothing? Will you lose the respect of the older children?
Have you thought about what happened to HaWho and her efforts with her H? She is one of the best DBers on this board, but in the end, the wild card is the MLC spouse.
Your W is too far gone right now.
If you have not done so, please go and read ParaPsy's thread on the newcomer board. I see your "nice guy" wanting to swoop in at the first sign of progress and try to wish all of this away. Your W has not had a big enough wake up. She is not coming to you with humility. She is not asking your forgiveness or that of her kids.