Ok so for a 9 year old strategies might be:
1. Ignore the hair apart from making a hairbrush available and saying: "here's a hairbrush, in case you want to brush your hair"" No further comment, leave the brush available
2. if you ask her to do something (make sure it is worth asking for, is hair worth it??) say:
- "** needs doing because **. When you have finished that game, please do it"
- If she ignores that when the game finishes say "** needs doing because***. I asked you to do that when you had finished your game. You ignored my perfectly reasonable request. Please do it when you finish this next game. If you ignore me again, I will remove your device until it is done"
- if she ignores again, remove the device; refuse to join in discussion; just keep repeating "** needs doing because. Please do it! When you have done it you can play on your device again!" Repeat, repeat, repeat. Do not engage in discussion, justification, responses to "clever arguments!
- if she rolls her eyes, mimics you etc say "That is rude and very hurtful. I will NOT put up with that rudeness and unkindness." Then walk away. When she asks you for something/needs something say "I told you I will not put up with that rudeness and unkindness. I feel very hurt." Walk away!
Alternatively say" That is very rude and hurtful. I will not out up with that. I am removing your device until you show me you can behave properly!" And do it. Then repeat, repeat, repeat, do not engage in argument!
You could quietly get yourself some lunch, not get her any then when she asks why say "You were very rude and hurtful to me. I got myself some lunch to cheer myself up a bit! I didn't ask if you wanted any as I didn't want to be treated so unfairly again!"
The point with all this is her getting consequences for her rudeness. She is treating you like a doormat and needs to see that you are not one. Also, don't threaten her with "Mum and Dad". You have to deal with this in order to develop her understanding of her relationship with YOU.
Good luck 