Having had this with my little brother I want to just put out my side.
No I wasn't right, but this was how I felt. (I had an older sister too)
If I did something/got something then he had to do it/get it too. Despite that he was 3 years younger than me, and even if I'd been told it wasn't fair if I got it before the age my older sister (also 3 years older) had it. It then became not fair for him to be the only one not to have it.
If he started something I did, I felt I couldn't ever be seen to be better. If I was clearly better then it was natural because I was 3 years older and he would ultimately be as good; if I wasn't then he was an infant prodigy and going to be brilliant.
Everything I did, he had to do (which wasn't true of my big sister) so I felt I constantly had him treading on my toes. Sometimes things I'd fought hard for years were handed him on a plate as it were.
And to make things worse, he wasn't even grateful. He complained; would say things like "well I suppose I must do X if you want me to" and never was satisfied with it.
My mum met any discussions with me with two comments "he's going through a difficult time" which she used whenever he was being awkward from aged about 8 till he was at least 28. Or a wail of "but he's your brother". Which just made me think "yes, and I'm his sister and what do I get out of it?".
I felt he could say or do anything to me and dm was afraid of telling him he couldn't-she would always come to me after an arguement and ask me to apologise/back down simply because I was much easier to deal with. I don't think she ever went to him.
I also felt that he was treated as the same age as me for a lot of things (eg bedtime dsis had later, he had same time as me) but then if jobs needed doing suddenly he was too little to do it. And on the odd occasion he was made to do a job he just picked fights with everyone and stormed off in a huff-and then wasn't made to do them. Nor got any repercussions for not doing it-indeed me and dsis usually ended up doing it anyway.
Now you're probably reading through this thinking "I don't so that. I'm fair." But the thing is that my dp thought they were-or at any rate the times they weren't were justifiable. I know because I've tried to discuss it. I didn't feel that they listened to me when I had complaints, and I was penalised for being the easy one.
I would: Talk to her on her own. Don't go into "this makes me so upset" mode. It really won't help how she feels towards him.
Listen to her. If she says something you really feel is unjustified, then talk it through why she feels that way. I know I over reacted on some things because of history. It may be that something small had built up into something bigger.
Make sure for a time that if you ask her to do something, you ask him in the same breath. If you wait until she says "I'm not setting the table unless he gets drinks out" then she feels that you wouldn't ask him unless she says something -so she will say something, and also feel put upon.
Let her feel older. Do things with her that are suitable for her age and not his. If she asks to do something don't always take him too, even if you think he'd enjoy it too. Or if you really want to take him you could make it an extra treat if he comes. "We could go on our own for the morning, or what if dbro comes then we could have lunch out and make a day of it".
Make sure things she does sometimes are just for her (and he has things just for him too). And if they do the same then praising him up to encourage him can feel the same as saying to her that she isn't any good at it. No I'm not saying that you can't praise him, but don't assume becasue she's achieving higher she knows that she is better. I certainly didn't-only as an adult have I realised that actually I was so much more talented at some things he got praised at that dm assumed I knew. I didn't, and what the conclusion was that I gave up tryng and ultimately gave up doing it, because they was a less embarassing option than having him overtake me, which was what I thought would happen.
If she tells you about something she thinks is unfair/has upset her. Don't dismiss it as a silly little thing that can't possibly really upset her. I can see as an adult that some of the things that upset me were luck of the draw/really didn't matter, but it didn't stop them hurting at the time.
And don't throw things at her that you think she has better. My dm used to tell me how much luckier I was because I had a good friendship group. Now the thing was none of us found it easy socially. Dsis was unlucky in her year group, but I worked pretty hard at mine. Putting myself out for people and going to do things when I was all knotted and shy inside-forcing myself to do them because I wanted to be friends, but dreading doing them. Dbro made no efforts and really seemed to go almost out of his way to refuse "Why do you think I'd want to do that?" I remember him saying down the telephone-and that was an activity he would frequently ask dm (who hated it) to take him to. Yes, he was shy and found it difficult, but my feeling was that I made the effort and got the rewards, and it was unfair to throw that back at me.
Oh and one last thing:
If you do discuss things and come up with a plan of action, Do follow it through, don't give up because it's awkward.
We once had a long discussion and I brought up something that was blatently unfair-to the point looking back as an adult I can't believe they hadn't realised before I raised it.
They totally agreed with me, and said they would change it. Well he made such a fuss that lasted almost 2 weeks before it reverted back. And yes, both phrases "He's going through a difficult time" and "he's your brother" were used when I objected.
But I generally had a happy childhood, felt valued and loved by my dp. I'm condensing all the things that I found difficult into a post.
What I got from your post was entirely about how to change your dd. Now it may be all her, but what I want you to consider is that it isn't necessarily all her, and she may be hurting over what, to you was so small you have forgotten it. Sanctions for her behaviour in that case may stop the behaviour on the face of it, but will just drive the feeling underground which will have far worse effect in the long term.