Chewbacca is spot on!
All kids go through periods of being rude. It is the nature of children to do so.
With my children, I simply look them in the eye and say very calmly "you are not allowed to speak to me like that" and move on. No guilt trips, no punishment's, unless the behavior escalates.
If my children choose to continue to engage in their behavior, I ask them to take a break from me (essentially a time out). Once they have calmed down they return and I make no mention of the incident again. It is good for them to know that it is OK to make mistakes, I will still love them and wont harp on it further.
Children need to be taught how to treat you. Once they figure out that you will not accept it, they will mostly stop.
For me it has worked. My teens and I are able to have polite conversations, even if they, or I, have made bad decisions or we disagree.
I learned this from my favorite aunt when I was a child. When I was at her house, I knew I was expected to behave a certain way. She had a house full of antiques and glass everywhere and would always tell me that she has never put a single breakable away and has never had anything broken. Not that we didn't try to touch things, but when we did she set the boundary. It didn't take long for us to figure it out.
Interestingly enough, she also told me how she got her kids to eat vegetables. She would serve 2 vegetables at dinner each night. One the kids would like and one they wouldn't. She gave them the choice. She said eventually they would get curios and try the other vegetable. Now they eat vegetables.
We once were staying with her for a week while my mom traveled and we decided to make a cake. Well, as kids do, while using the hand mixer we pulled it out and ended up with cake batter all over everything. We just KNEW we would be in trouble. She remained calm, never showed impatience and handed us rags and a mop.
Kids need boundaries and routine, but they also want to be treated respectfully and with autonomy. 40 years later and her calm dealings with our choices still resonate.
Kids (and people) will remember how you make them feel, eventually internalize it and pay it forward in the future. Or so I hope.