My first thought is to get yourself in a good place before you can work on your R. Your mentioned that your H is an alcoholic. Is he getting any help for this? Are you still on medication? Please recognise that you were ill and therefore did not deliberately set out to damage your M. So don't blame yourself for that .
The positives are that you are both in counselling and he says he still wants to be married to you. The OW is a complication but I think your first focus should be yourself. Have you discussed OW in your counselling sessions? Did you have a transparency plan re his not contacting her?