I think the problem is not you not being assertive, but the fact that pretty much no one wants to work on a Sunday in a salon. Ask yourself this- why should the staff do something extra for the business, if the business is not going to do something extra for them?  If they are already working full time, why can't they do the car accident stylist's clients during their regular scheduled hours? Maybe you just need be more flexible and try to understand the staff's point of view better.

You might disagree but, let's be real these people can go to any chain salon and not work Sunday early afternoons. How many chain salons have stylists with 90% requests? That's not realistic. She doesn't have the leverage to tell them what to do.  

Let's say you do hire someone new, you have to train that person, and if they are just out of school that training could take quite some time. Most people who work at chain salons go there right out of school not after being experienced because they want to start working on clients right away, don't want to assist, and want the benefits. It's not easy to find someone who will work on Sunday.