Tuesday: I would double check with your local agency,but I would say,no,she has no rights to the dog at this point...quick question...is YOUR name on her dog license??
I would say that...since you have been taking her to the vet,buying her food and providing the daily care,she is YOUR dog...If you can prove,by receipts or even just the vet records would work that YOU have been the one providing the care,she really has no claim on the dog anymore and you have every right to keep her...
Now,onto the first part of your post...YOU have to go out he door first..YOU have to come in the door first...If you know all about the alpha dog,then you know by allowing THEM to do ANYTHING first,you are giving THEM alpha rights in YOUR home.
How has the exercise of the shoes/keys thing been going??