If you were validly and sacramentally married at the time, his act does not invalidate your marriage, but if the Archdiocese approved the lack of Canonical Form request, your marriage probably wasn't valid.
I can't really provide any valuable advice as I am single, not married. It's best if you get pastoral advice from a priest in your area who is faithful to the Church's teachings.
On the face of it, I don't understand why you would want to remain together with him. It doesn't sound very practical to marry someone with domestic abuse and alcohol issues, especially since it appears he has no interest in addressing these issues.
Marriage is a sacred bond, a sacred Covenant with God, and a lifetime commitment. It should not be taken lightly.
I would break off the relationship immediately, and if he tries to come back, tell him you have moved on in finding another single faithful Catholic man, like in your local Catholic parish.
It's best to talk to a faithful priest about this and take his advice.