I was talking to a co-worker about discipline lately as my 5 year old son is taking to ignoring us and not responding to a direction right away. He said he and his wife went to a parenting class and what he said made incredible sense.
First, you shouldn't let your daughter get away with it. It may hurt your feelings but she isn't "getting" it, nor is she likely to if you don't take a more hard line.
The gist of this discipline method is that you never repeat yourself. Tell her ONCE and if she does not respond immediately, she endures her punishment. The rule for parents on this is that they have to sit down ahead of time and explain the rules. When you then go to give her direction, you call her name and make sure she answers first. Then when she answers, you give her the direction. She has ONE chance to do what you say, and if not, the immediate consequence is carried out. Whatever punishment you decide fits the situation.
How does this relate to what is going on with her and you now? She is being disrespectful and you are allowing her to do so. She may not ever understand how she is being disrespectful until you show her consequences for her actions. A simple time out, grounding from a toy, etc, will be quite effective. She isn't going to change if you don't actively do something to change it. This does mean it's a lot more work for the parents than the kids though. We have to follow through, and sometimes that means interrupting what we are doing.
I was amazed to see when my son started school at how well behaved he was in school, and when we asked him about why it takes us "to the count of 3" to get him to do something and why he does it immediately for his teacher, he said it was because she (in so many words) meant it. And do you know what? He's happier knowing his boundaries. Kids are so adaptable and they do like structure. If you start calling her on her attitude toward you and punishing her for it - and do it consistently - she will get it, and I'll bet she get it quickly. Good luck!