It seems to me that even though he loves the puppy, he doesn't like the idea of the day to day care of her so much. He offers to keep her but knows he can't actually do what needs to be done so you are stuck doing it and miles from home which just adds to your responsibilities and stress.
It's almost worse than child custody!!!!
If he won't carve out chunks of time to have her, then maybe he doesn't need to. She will adjust just like kids do. If he thinks she likes you better, than maybe she does!
Go dark, take care of the dog by yourself, and cut communications since it's all about the dog anyway at this time.
Hopefully the weekly EMDR will help him deal with more of his stuff and he will overcome his lifetime coping mechanisms that are so self-destructive.
This has to be beyond painful. In some ways it must feel like another D since you were together so long. I'm so sorry. This stinks!
T19 M15 S19 XH47 M43 bomb12/4/07 PA5/07 S12/26/07 D final 11/17/08 Back together with no defined R 05/2010 confused....to say the least!!!