Welcome to the world of dogs! The Yorkshire Terrier is a nice breed, and I bet this nice dog misses your mother.
I'm assuming your mom's dog is healthy; if you and your mother aren't sure about that, take her to the vet to make sure there isn't a physical problem.
If she's on leash most of the time in the house, can you make time to take her to your fenced yard (or a dog park, if she's used to that) and give her a little more freedom? Can you or somebody in your family take her for a walk around the block every day, or twice a day? She must stay on leash for that, since you're not her owner.
At your mom's house, are there any doggy toys? Any special blankets? She might feel more comfortable having some familiar things with her. Do your know what her home routine is like? Ask your mom. Familiar routine may help; she may be saying, "I'm supposed to be doing (something) right now - why aren't I?"
What sort of obedience training has she had? Can you run her through her paces every day? Would the rehab center allow you to take her along when you visit your mother?
Believe it or not, dogs are like little children! You know what a child would do if removed from his/her home and family and plunked down somewhere else. Dogs need attention - who doesn't? - and, being pack animals, they need to know that their leader (that's you, temporarily) cares about them. So talk to the dog and give her attention. Pretend she is a three-year-old human house guest who eats very strange-smelling food. It may surprise you, but she really needs this attention. If she feels more secure of her status in your home, the whining may diminish. There may be habit involved, too, but I think attention will help.
I wish I lived closer to you. We're a very "doggy" family and we would love to have her over to play!