I really really feel for you OP but I do need to be really honest with you in saying that yep, whilst he was in recovery (which is what he was when he was not drinking and prior to relapse) but not in 'active' recovery - meetings, sponsor, commitments, working the steps etc or all via the Smart Recovery route if his argument that AA isn't for him - then this relapse really was only a matter of time
I have someone unbelievably precious to me who is in recovery but active recovery, working on his sobriety one day at a time. I am beyond proud of him, he has fought and ought to free himself from the trap of active addiction. He recently picked up his 90 day chip and is now over 100 days into his recovery (which is why Yselute's bollocks really wound me up, as someone who knows as little as that about recovery should say nothing if they don't know what they're talking about)
I urge you to concentrate on your plans for you and your child, as what he chooses to do or not do only he can decided - he has to want sobriety and recovery to achieve it and his best bet would be to hit a meeting tomm (they're EVERYWHERE so he can just google) and pick up his 24hr chip - and then lob himself into the programme as if his life depends upon it... as it really actually does depend on it.
You do need to work on the assumption that this relapse is either permanent or, if fleeting, is still on very shaky ground in the absence of going into active recovery; hence why it is so very vital you focus just on you and DD.
It is beyond traumatic living with an addict, my heart goes out to you and please ignore the twats who are saying you are 'playing games' or other shite like that. Please don't let them stop you posting either - if I were you I would ask for thread to be moved to [removed by MNHQ] and the supportive posters will stick with you over the next days and months 