Good job Ken. I know it hurts right now, and you are likely terrified, but trust me it gets easier from here. Your wife is deluded if she thinks this guy is going to solve her problems and keep her in a perpetual state of bliss.
Reality needs a few weeks to sink in.
The only slip you made is validating her not loving you. Ken she does love you, she's addicted to a fantasy right now and has no idea what she's doing... do NOT support her saying she doesn't love you.
This is how you handle that :
WIFE : I don't love you... I haven't for a very long time
YOU : Love isn't a feeling, its a conscious commitment two adults make to raise children and support each other. And right now you are doing a miserable job of both.
WIFE : I want us to stay friends for our kids.
YOU : Right now you don't deserve a marriage or children.
WIFE : Why do you have to make this difficult?
YOU : Everything I am doing and I have done is for you and our children. You will have to learn about this mistake the hard way. Unfortunately me and our children will be the ones paying the price for the next two years until this affair ends and you realize how selfish you are right now.
WIFE : So now what?
YOU : Please leave. Stay away from me and our children, they need adults who set examples of commitment and maturity, not selfish children who chase fantasies and tear households apart.
WIFE : I love <om>
YOU : I realize you are foolish enough to believe he's the better man, but there is one important thing that you aren't acknowledging : I wouldn't do to this household alone what he is doing to TWO households. You can walk out of here to be with him but despite everything I would be ashamed to be in his place right now... .
