So .. Tell her you dont like her being rude and set some bounderies, you dont say that form the Rudeness takes,is she giving her opinion or what ?what are the rude things.At 10 they sometimes test the limits have a chat with her say it upsets you then make sure she has repercussions for the behavior loss of a privilege or something if it is very rude ,a time out.
I don't want to start out negative, but you get the child you raise. Children's behavior is conditioned and learned from Day One. No child is born "rude"; this is a learned behavior over a period of time. They learn it by closely observing and modeling the behavior they see, hear, and experience at home, and they continue to practice the behavior because it is successful in getting them what they want or need. Tolerance of this type of behavior over the last 10 years has created this situation and you cannot reasonably expect it to change now just because the behavior is more annoying as she is older and it is more intense. It is going to take some work to reverse.