Hopefully it's just a two year old tantrum type phase and she'll grow out of it. I don't think dry shampoo works on any type of hair--I remember my mom trying it out--mmmm, greasy hair with powder on it!
I think I used to wash DD's hair at that age by getting her to lean back in the tub and just rinsing the tub water through her hair. No shower sprinkling or splashing. She's always been CG so I didn't have to worry about shampoo, its just conditioner in the water and I'd be putting more on her hair anyway. My kids HATED getting water on their faces at that age and still don't like it. They are teens and still usually choose baths over showers