Good on you Lucy, it's good that you won't let her get away with bad behaviour. You are setting a great example.

My SDD was starting to turn into quite the little so and so too. She spoke to everyone around her like dogs. We quite like each other, but I pulled her up short and sharp one day when she was rude to her dad. She has never been rude or spoken back in this house again.

There are plenty of other issues still, but never rude (near me anyway)!