I think you may be a bit confused as to what is a boundary and what is an ultimatum.
What you have said to him is an ultimatum. He cannot live with you unless he goes to AA. You have NO CONTROL over what he does or does not due.
A boundary for you could be:
"I will not be with or live with anyone who is not sober and/or clean."
What he does about that is then UP TO HIM. Whether he chooses another rehab, AA, SMART, CBT, Life Ring, AVRT, or any number of other programs, IS HIS CHOICE.
Oh and btw, NONE of those choices will work until he WANTS RECOVERY more than he WANTS to DRINK and/or USE.
I will tell you what my parents and family's boundary was for me and said to me:
"You are no longer welcome in our homes, we will no longer talk with you, if you come to the door it will be closed in your face, if you call on the phone we will hang up, and if you attempt to steal from us the police will be called. This is YOUR PROBLEM YOU FIX IT."
That was January 1, 1979, I was 33 1/2 years old, and YES they meant it and YES they stuck to it.
It took me 2 1/2 more years to find recovery and the last year and 1/2 I lived on the streets of Hollywood. I was 3 weeks shy of my 36th birthday when I died in the ER of Olive View hospital. That was 30 1/2 years ago and I have been sober and clean since.
What I am saying is YOU cannot FORCE him by words (ultimatums) to do anything. You can only state what is and is not acceptable to YOU.
Maybe, just maybe it is time to go NO CONTACT for a few months or longer and just WATCH his ACTIONS to see if he is seeking recovery or not.
J M H O
Love and hugs,
ps: most rehabs use the AA 12 Step model, so that if one wants recovery badly enough and goes to a rehab they are getting AA about 16 hours out of each day. However, I do believe that there are many more in AA that did NOT go to rehab, than those that did.
Also since he says he now wants 'help' he has been around long enough to KNOW where to go to get it. You cannot help him this is HIS RECOVERY.