My husband says just the opposite- we should push and push and push.. I, frankly just think he is using this pushing as a way to push my son away so that he is not taking up my time.
Your SO sounds like he resents your child living with you and is worried that it could be forever. From what you've said, it sounds like you're also disturbed about the latter. Short-term, he does need help from you, but all three of you might benefit from agreeing what "short-term" is and from your son becoming engaged in developing his own long-term life plan.
Whether your husband chooses to drink or not is ultimately his part, but working on the family is everyone's part. It's good that you're working this out with an expert both in family and addictions therapy.