Don't you just hate when your parents are so Stubborn?
Well, first of all, sorry that you had to go through that.
Considering the age your yorkie is at, I would certainly give in , regardless if I did nothing wrong. I would do anything to see my dog before he *passes* away from his long-lived happy life. Fact is, your parents will always be your parents... show them how mature you are and give in , I'm sure they will look up to you with good thoughts & show them that they've raised a great person and then guilt will be knocking on their door lol!!