I agree with the other posts that Yorkshire Terriers are extremely low on the allergy-causing list. Yorkies are actually on the "recommended dogs for allergy people" list:
http://www.dogbreedinfo.com/allergy.htm
I would first see if your dad would give a cleaner dog environment a try -- do the weekly baths, daily brushing, and frequent house clean-up. Remember that is is not the dog hair people are allergic to, it is the pet dander or old dead skin cells that are constantly being shed. Frequent vacuuming and even a good air filter can help quite a lot too. There are also special shampoos that help remove the pet dander. Here is an example, although I have never tried one:
http://www.theallergyreliefcenter.co...FTOKEN=8052489 See if that helps.
If not....and your dad still believes your dog is the problem, I would ask if you could find a temporary home to "test the theory." Find a friend or family member that would agree to take your dog for a couple of weeks. Then see if dad does have any improvement. It is possible to be allergic to a yorkie, but how can he know for sure without a test.
If the temporary separation does show improvement for your dad, then you will have to find another home for your Yorkie. Maybe someone who is close enough that you can still visit and maybe even someone who would consider letting you take her back when you have a home of your own? Good luck to you, your dad and your Yorkie!