I'm pre-vet also.
It is just fine to have a Yorkie, but not all college students can handle it. But a pre-vet really should be able to figure out a way for the most part.
That said, I can understand a breeder not wanting to sell you one (and I'd be tempted to go to a BYB, honestly
).
I don't have to do everything myself, so it is possible for me to have a doggie. Before getting one though, consider:
Who pays the dog bills, esp. what you move out and make no money (vet school)?
Will you be able to afford to live off campus in vet school?
You live with your mom and you said you aren't happy with her over at least one issue. You are a pre-vet and undoubtedly have opinions about how this dog's vet care should go. Does your mom agree? Because if not, it will be a source of tension...
You only have school now, but will have to volunteer and/or shadow and/or work and/or research and/or TA and/or do your extracurriculars, etc. How many hours a week will you be gone then?
In vet school, there won't be time to go hang out at night and such. You'll have to go home to the dog most of the time.
It is not a bad idea. It has the potential to be very difficult.
ETA: No way do I study three hours for every class hour either. I love my life too much for that.