If you go out of the gated area, there should be a terminal there, you have the option to lock Dog in there, which is what I had to do since I ran into the same problem, just lock his @@@ in there, lol.
you can also play the recording you got earlier in the dlc, that will change him to god, and convince him to stay.
I never enlisted dog the whole game, just preferred conversing with the more intelligent schizo. Still had to get him meat by killing 2 ghost harvesters. They do show on the map though so it's pretty easy.