Well, first, I would like to say that you are quite well-spoken and seem intelligent. How old are you exactly?
Second, as a mom, I can think of a couple of reasons, but, again, as a mom, I'm not sure you will quite understand until you are a parent. It's one of those "you can't know what it's like until you experience it" things. Nothing I am about to say is meant as insulting or condescending, just trying to be straight forward and honest with you.
1. You say you are willing to take care of the dog for its life. A Yorkie can live quite some time, and as a minor, even though you may have the very best of intentions, the truth is, you cannot know what you will be doing ten years from now.
2. As a minor, even if you do all the work, the responsibility of actually making sure it is all actually done (feeding, bathing, training, vet care) will absolutely still fall on your mothers shoulders. Even if you and your sister do all the work, your mom still has to be the one checking to make sure it is done.
Hopefully this makes sense to you, as I tried not to ramble. Just remember, when you are on your own, you can make whatever decision you want. Waiting is hard, but you can always take the waiting time to learn even more about the breed you are interested in. You can never know too much
