So sorry for the reasons that bring you here, but glad you found SR. It may be a bit quiet for the next couple of days with the 4th of July, but you will find lots of support.
Early recovery is a struggle both for the addict/alcoholic and for the friends and family. It takes quite awhile for things to change. I think you are doing the right thing to keep your distance. Let him work with a sponsor and other sober friends to work out his issues. Certainly it is no part of AA or any other recovery program that friends and family are supposed to "take care of" the recovery addict. If anything, it's learning how to live again and be responsible for himself while maintaining sobriety.
So maybe you and your husband can practice letting the phone call go to voicemail and not jumping when he says jump. As a general statement, many addicts are all about instant gratification, and learning that things don't happen that way in the real world is a part of recovery too. So believe it or not, standing back and letting him find his own way is truly being supportive!
I really hope your BIL decides to really work a program of recovery and stay sober.