Read the DB and DR book! I have been there before. My H did (and is still doing) the same - EA, refused to stop contact, is still in touch with OW. I did all the same things - beg, plead, not eat, anxiety. Felt like dying. But right now, I have been able to somewhat go on with life, and it gets better with time. It is a roller coaster though.
You have children, so please take care of yourself for your kids. He is still home and does not want to leave, so you have a lot of positives.
One of the things that helped me is the knowledge that most affairs don't last forever.
For now, take a deep breath, and do not do anything drastic or impulsive.
Me:49 H:45 D:12 M:14 T:18 Bomb: 6/26/10 EA: 9/3/10, fizzled out slowly, now ??? 11/5/11 Retrouvaille Finally piecing.... Its peaceful at last, but we got a looong way to go