When I moved out, my landlady was a total B***h about my pup Twilight. At first she was like "ok your pup can go in and out" and all that. Then her cats got kind of fussy and started to pee on things (they do that when they are upset) and she said, mind you in the middle of WINTER that Twilight had to go outside and be locked out there. If I wanted to spend time with her I had to go in the garage (freezing) or outside (freezing more pfft). I finaly let my mom take her because I knew that mom would let her stay indoors. When I moved to a different place I was going to take Twilight with me but I realized mom was so attached and Twilight was doing so much better. I let her stay and visit constantly. I think that if your dad can provide a better home (and it sounds from your description that he will) than your moms place and you're allowed to visit frequently, then you should let your dad keep her as he and the pup seem to share a good bond. Thats just my two cents.