Is this typical 9-year-old behavior?

I am 30 years old, my sister is 9. My sister is still in the "me, me, me" stage and she is very disrespectful and selfish. She's going to be 10 in December, but when I spent the last two days with her, she's poking me constantly, putting her face in my face and says "I'm a kid, what do you want, this is what kids DO!" and she walks ahead of me and my mother in stores - almost straying away from us and getting lost. It's like she's really using the excuse that she's a child to constitute her refusal to try to grow up.
My mother reprimands her, as my mother is extremely stressed and yells at her to think about what she's doing and realize that life isn't all about her being a child.
But should my sister be trying to grow up and be caring of others (even more so, her family).
She's asked me on occassion if she can sleep over my house, but she already picks fights with me and can't spend time with me without getting an attitude if something doesn't go her way. And she is, in fact a drama queen (as my mother has confirmed) and has been one all her life.

Is this typical of a 9-year-old and how can I tell my mother that I can't have a sleep over with her knowing something will erupt and she will cry if she doesn't get what she wants or she takes something the wrong way?