Did the vets say anything about her teeth? Did they say WHAT they thought was wrong with her?
Usually drooling and slobbering and hardly being able to chew her food, would signal a dental problem, or mouth lesions, or ulcers.
This sounds like a systemic type of disease that could be affecting her. How old is she?
Loss of balance and losing her fur, also seems to indicate a disease state of some kind, but did you have her bloodwork done while at either of the vets? You should ask for a copy of her bloodwork, if you had it done. Always do that. I had my cat's bloodwork done recently, got the results back, and the vet told me things that were wrong with my cat, and I asked for a copy of his bloodwork.
Come to find out, someone made a mistake and put down that my cat was a DOG, and so the blood results were all different in some areas, than if they were compared to a cat's values. Fortunately, I keep copies of their records, or we never would have discovered this big mistake. It made a difference in his prognosis, also.
Please post back on how old your dog is and what type of dog. Maybe I can give you some ideas, although I am not a vet, but one of the vets in the group here may also be able to help you.
God bless and good luck!