Dont allow him to wind her up in the first place, then you wont have to deal with her whining. Id whine too if my older brother was picking on me.
I think your right ignoring bad behaviour does go a long way but sometimes some bad behaviours cant be totally ignored, like with your dd being annoyed like that.
Give him 3 clear chances, then its time out (or any other type of punishment that has an effect, taking away tv time, or playing out or whatever it is they like to do).
Keep doing it, no shouting, no ordeal. Even if you do it 1000 times in an hour, he will get the message say after a week, that he only has three chances to sort out his bad behaviour or its bed/stairs etc or wherever you like to put him or whatever punishment you choose.
The book tells you how to do this much better than i can - but the jist of it is keep calm, repeatedly count his three chances until he knows that three means business. Dont allow yourself to get cross, keep calm, count him to the 3 then put him out somewhere or whatever, but enforce punishement at three with no shouting from you.
Your daughter will appreciate, you will feel calmer and he will eventually get the idea of it.
I PROMISE.
You must be consistent and stick with it for at least a coulple of weeks. Both you and dp.
When i started this, i was counting to 3 with dd1 continuously for the first week or so, nowadays, i just have to hold up one finger, then two, then she knows not to go any further.
Sometimes she does push it all the way still, but far far less frequent.
Its such a shame, that she will push it to two, maybe as time passes she will drop it at one. There is always hope i spose.
Its really the back chat that i struggle with these days. I mean she does wind up dd2 but she knows she has to stop when i start counting.
But the back chat is very anger provoking for me.
For some reason, kids just want to push you to the edge just to see how far they can go i think. Mine do anyway.