I guess they don’t help her shower at all? The problem is that she’s probably really offended when the staff tells her that her hair needs to be washed, like anyone would be! Is there a hairdresser on staff? At my community we have a hairdresser come in frequently. My residents LOVE getting their hair done (as most people do!). Maybe you could set up a schedule with the hairdresser so that your mom is “getting her hair done” twice a week. Really, the hairdresser will just wash it.
If there isn’t a hairdresser, could the staff get more involved in her shower? Alternatively, they could offer to “do her hair” themselves. It could be a special event where she has her favorite shampoo and products nearby.