Wow, that's a tough situation! I feel sorry for you and I understand what you mean about it being a pain in the butt when she comes back and is almost "untrained." How frustrating for you. Is there no getting thru to your boyfriend about her just staying in ONE house (i.e. yours).
I do think it makes for more stability for the dog to stay in one house. I see no problem with her going with you every time you go to your boyfriends house, and then just coming back home with you. If she was given to you as a gift, technically she IS your dog. It sounds like you guys are bonding really well. If your boyfriend insists on doing this switch-a-roo thing... you should make it clear he NEEDS to upkeep with her training and not let her get away with everything (funny the GUY is the one with a soft spot for a lil' girl yorkie
typically, huh?) So she at least has some consistency in her life. I know there are couples who have split up, and actually get "custody" of the dog and do the every other weekend, etc type thing just like a kid. So it is possible.
I kinda know what you're feeling because I spend maybe 2 nights a week over at my dad's place (they have 2 other dogs) and whenever Jackson is over there, all my rules go out the window because my dad totally spoils him and doesn't really have any rules for his dogs, so of course Jackson follows. But I'm always sleeping there with him.
Good luck!