V.R.
Hi J.,
I'm a 48 year old mother of an only 12 year old girl. Don't worry too much! At 9, believe it or not your daughter is experiencing hormone changes and mixing with other kids going through similar changes who are all trying new things out. I wouldn't punish too much. Just make clear what your expectations of respect are, for example if my daughter says something in a rude or snappy manner, I repeat back to her what she said in the way I expect her to say it. So, if I ask her a question like "Have you finished all you can eat?" and she just responds with a curt and surly "yes" (which she did just 10 minutes ago), I'll say straight back at her "Yes thank you Mommy", and 9 times out of 10 she'll repeat that back to me! Try taking deep breaths and slowing your responses back when you feel like snapping or shouting at her.
I don't know how much TV your daughter watches, but I found that if my daughter was watching certain types of programs where children were sassy and "cute" towards adults I would get a lot of that behavior from her. I told her that if she continued to behave in that way she would not be allowed to watch those programs. I also pointed out that those shows seems to indicate that adults are stupid and kids know it all, which is NOT how life really works.
Like I say, it's a matter of telling her what your expectations are and how you want her to behave. I also know that if you want to be treated with respect you do have to live that way yourself. Children learn so much from the environment around them, and if they see their parents behaving disrespectfully towards each other or towards others they pick up on it. I'm sure you don't roll your eyes at people, but it is useful just to check in with yourselves and think how you behave to the world.
I have found the books of Anthony E. Wolf very helpful. I know your daughter is a little younger than mine, but it may help you to understand what is going on with her if you read his book "Get Out of My Life, but first could you take me and Cheryl to the mall?". His other book "The Secret of Parenting" I also found useful. There are lots of other books out there, but those are two that were recommended to me that I found good.
Hope this answer isn't too long winded and that it's useful. You are at the beginning of quite a roller coaster ride with your daughter, but I can tell you that the years of 10 and 11 with my daughter were really quite lovely. Enjoy every moment of the good - it provides a great foundation for the rocky road of adolescence which lies ahead.
V.