Maybe you take after your grandma in your love of animals?
We have 4 dogs, 1 cat, 4 snakes, 1 lizard and 2 fish tanks here right now. We have had hamsters, guinea pigs, a different lizard, etc in the past. LOL
I love animals. Most of the dogs are mine. Everyone in the house has a snake, except me (they bought me one for my birthday several years ago, but it died right after we got it). My 14 year old son has 2 snakes. My daughter owns 1 puppy, 1 cat, 1 snake, 1 lizard of the animals in the house. My husband has the fish tanks and the big dog is technically his and our puppy is both of ours according to him. Teek (my 9 year old Yorkie is mine), although really all 3 of the boy dogs are really mine. LOL They adore me.
I am sure something will work out. Maybe your Yorkie will win over your mom
Teach him to behave and teach him tricks too. Work with him about 5-10 minutes a day (twice if you have time) and teach him sit, stay, down. Then branch out to things like come (I use the command Touch), and place (go to their bed), Crate (if you use one), then teach tricks, like up (stand up), Sit pretty (beg), crawl, roll over, anything you can think of. The more trained he is like that the better dog he will be, I promise. If you train him well, maybe your mom will decide he is a good dog and decide to keep him for you, or at least your grandma will appreciate a better trained pet while she has him.
The best way to teach a Yorkie is to praise good behavior and train them well. I will tell the puppies no, and take away things they should not have, but that is the extent of anything negative I do with mine.