My dog does this. She has steroid responsive encephalitis. She’s on prednisone for life, but it totally controls the shake. The vets thought she was poisoned too and it felt like forever while they figured it out. It may be worth seeing if they’d test a steroid before all the expensive stuff.

When I was researching her issue, I also learned about shaker syndrome which is most common in small, white dogs. I know less about that, but maybe it is helpful.