I've worked in a lot of food service, and these types of situations are fairly common. Standard professionalism is very different in restaurant work because it's so fast paced, hot, and frustrating. But this girl sounds like a spoiled piece of work.
Next time she rudely gives you some command, you could do what my aunt does when her 6 year old is throwing a tantrum and respond with "Well, that's not a very nice way to ask!" And wait expectantly for a nicer request. If she throws more attitude, just shrug and tell her that this is a place of work, and you expect her to act as such. Keep the focus on her behavior, and don't get roped into defending anything about yourself.
Alternatively, since she's talking to you like she has some authority over you, just respond cheerfully with "Yes, Mother!" She'll give you a wtf? look, and you can say that her attitude reminds you of Mrs Bates, so "Mother" it is! She's probably too young to get the reference, so if she asks who Mrs Bates is, just tell her to Google Bates motel. And then continue to call her Mom or Mother until she starts behaving herself.
I haven't found managers to be much help in these types of situations, unfortunately. But I have spent a LOT of time seeing this kind of thing unfold and am pretty good at disarming difficult people.