How can I best encourage my preteen to live up to her artistic potential?
To encourage a child to live up to potential without being overbearing, you must close the communication gap. You and your child speak different languages. She says one thing, you hear another, and vice versa. Try getting to know each other a little more. A deeper understanding of each other will lead to better communication. Better communication will give you the ability to encourage without being too overbearing.
The key to open communication with your child is seeking to understand what they are thinking and feeling through active listening.
Listen to your child just like you would listen to your friend. Try to understand what is going on in her life. Ask questions about her likes and dislikes, her friends, her accomplishments and her fears. Knowing that you know what she is dealing with will make her more receptive to your influence.
Listen for what your child doesn't say as much as what she does say. Is your child frustrated about the time it takes to practice the piano? Is there something your child doesn't like about her piano teacher? Does she lack ambition about piano specifically or is she lackadaisical in general?
Keep in mind that most preteens don't know what they want to do in life, so help her explore her voice: her niche, her groove, what she was born to do. Take her to piano concerts, get her a CD of a hip young pianist, find ways to reward her for what she does well, and she'll become a talented young woman in her own right—either on the piano or not. Let her explore all of her options, encourage but don't force and then accept her for who she is today.