It's good to have a DB coach and great to have a counselor. Working out, looking better are all wonderful things.
Consider going to AA meetings or being evaluated by an AA counselor. Many of the mistakes and stumbles in your marriage seem to center around actions that happened while you were drinking. No one wants to be an alcoholic, no one wants to be labeled. Knowledge is the best recourse. You can only deal with a problem if you acknowledge it.
It's also important to know your legal rights. Consult with several highly regarded lawyers and tell them your situation. It will help you regardless of the outcome.
Your wife wants children but will not have them with you because of your behavior. Hello.. big red flag... she doesn't trust who you are.
It's about you getting healthy. Do that and the rest follows.
