Hhhmmm. I am going to take a different stance here. Chances are high that if you agreed to joint custody,with you as the physical guardian, he will lose interest in a while. It'll cut into his drinking time, having the kids around for an entire weekend.
My exh is not an alcoholic, but when he came at me with the joint custody bit, I said "darn straight you'll take these kids, they are yours after all". It worked...took one less squabble off the table, and we ended up with our state's recommended arrangement anyway...similar to what others have described.
I played the reverse psychology game. It worked for me.