Dear Annie -- May I say that I am actually envious of this story? That your son had the trust in your love and abiding care to come and talk to you, that you jumped right into the situation with research and found a facility for his rehab, all of this is pointing towards a successful sobriety -- and life -- for your son.
I have a sibling who is alcoholic, and we've never been able to help her towards sobriety. Her story is what happens in a life without facing the monster of alcoholism. She is literally dying in front of us.
Blessings to you and your son.