"Here is the girl. Six years old. she’s got your eyes. Her mom wants to know if she [the daughter] can use this for her [the daughter's] acting reel."
It's a badly written sentence which is part of the reason you are struggling :) The "she" and "her" in the second half of the sentence refer to the little girl, not the mother.
(Well, the "she" could be the mother, actually, but it doesn't matter as much - what is important is that the "acting reel" is definately the daughter's!)
An acting reel is a an old-fashioned term for an actor's portfolio of clips of their work. Nowadays it would all be digital, but the term seems to have stuck.
A reel is any kind of circular or cylindrical device that we use to wind something one - rope or threadmost often, but in this case film. The best way to explain it is probably with a pic because a "film reel" is a pretty iconic image nowadays:
An acting reel therefore used to be a film reel like that, made up of clips of the actor's work. They would use it to show people to try and get more work.
As I said, nowadays it's not a literal reel anymore, but we still use the word.
I guess the little girl in your story is trying to put together a portfolio of her acting work so far, and they want to know if they can use the film the family is putting together as part of her portfolio.