I'm sorry, sho -- I can feel your pain oozing from your post. This makes me really sad for you and especially for your kids.
I'm not sure I have any specific advice I can give you, as to be honest I cannot relate. While I still loved my wife and wanted to reconcile while she was having her affair, I felt a lot more ANGER than I did wanting to hug her. Maybe it was the daily intel I was monitoring, but I had a much harder time with the "loving" half of "loving detachment" than I did the "detachment" part.
But you are NOT giving up by detaching! It is simultaneously the best way to protect YOURSELF while also giving you the best chance of re-attracting your wife. "Moving on" does NOT equal "giving up."