First of all I would get her off the sweet potato immediately, as this can cause skin allergies in a lot of bullies. As far as the demodex, it usually can be treated with antibiotics and not the poison dip. I am no expert in this but some people on here have dealt with it. This is some info I found on the net
Many veterinarians believe that all dogs have small numbers of demodex mites residing in the skin and that having a few mites is normal and common. It is when immune related -- or nutritional or environmental -- stresses impact the dog that visible skin lesions from mite infestations become noticeable.
Demodex is generally less severe than Sarcoptic mites (often called scabies) and in most cases is self-limiting -- that is, the animal is able to arrest the reproduction and growth of the mites and eventually repair the damage they do.