Hi loho sorry to hear you have your hands full. My 7 year old DD is really a handful at times so I totally sympathise.
My dd is quite rude at times but today when she tipped her chair backwards at the BBQ it was me who ran to comfort her (more embarrassment than pain - I think) and she clung on to me like a koala. Being in places where she does not know lots of other people or feels it is all new (like a museum we have not visited before) or at a friend's house who she does not know well, tends to bring out the little girl in her who needs me. Being always in familiar places and often in charge makes her rude and unpleasant!
So I am not suggesting you tip her chair over (!!) but rather that when you get the chance to be the caring mummy you build up a bit of capital on it and try and help her to see that you are her best friend/ally etc. Do some more stuff together.
I have no idea how close your relationship is with your DD and what other factors are in play but I would suggest if you don't do it already to build in some mummy and me time with DD, where you do some lovely activities and maybe (just maybe) this will help her attitude to you.
Encourage her to talk about how she feels and why she thinks it is OK to be so rude to you (I am assuming she is not rude to everyone else - well, certainly for me my DD is very polite at school and it is me and her dad who get the rude behaviour!)
I often say to my DD when she is rude to me, how would she feel if other children spoke to me like that; that having a mum she is rude to doesn't make her look big, it makes her look sad!
I think punishments etc are all very helpful but it also helps to help them work through it.
I'd also suggest you find out if anything is going on at school/brownies or whatever that might be making her rude. For example is she being left out, bullied or has she fallen in with a few girls who talk to their mums like that too? Sorry if this is too obvious. Sometimes we do miss stuff because we think we know our children so well and yet they can still surprise us!
If you already do all that then I don't think I can add much!
Just ideas.
We are seeing the schools link worker about our daughter?s attitude so we are getting some outside help because we have reached the point where we think we need it. So sadly I don?t know much but I do sympathise.
All the best.