Hi there...wow when I read the story you wrote about your DD regarding piano and gymnastics and the expectations for those I was amazed at how it paralleled my childhood. I'm so glad you're rethinking your position and here's why...simply from my own experience of course.
It's true that pushing a child can de-motivate them to the point of them questioning if they're ever good enough. I always dug my heels in because I too loved playing the fast paced piano pieces but I wanted to play them my way...not the teacher's way. I was considered gifted in piano and athletics. Gymnastics was the same for me...I was pushed by my parents (particularly my mother) and by the coaches. They wanted me to try out for the olympics, etc. The pressure to perform to such a high standard continuously not only for a teacher and/or coach as well as my mother's friends on que is really a set-up for failure. My mother used to call me a quitter when I wouldn't put on a piano concert for her friends and she would guilt me by saying I was refusing God's gift to me.
I didn't enjoy playing with pennies on my hand nor did I enjoy the rigorous hours of playing each and every day with the metronome sitting on top of the piano..."click, click, click."
I see the same personality traits in my DD and even though I have had some real negative experiences with pressure...it is so hard not to do the same thing. Children do not see the world through an adult's eyes...they see it through their own. They haven't experienced what we have and as parents, because of our own experiences, we try so hard to help our children avoid the mistakes we made, etc. I have had numerous opportunities to capitalize on my gifts, particularly in music, and unfortunately I refused them all simply because of my own angst. Now of course I regret those decisions and certainly don't want my daughter to fall into the same trap. It's a fine line between a gentle nudge in the direction we want our kids to go and the push that I have referred to above. It's hard to find that balance.
I wish you the best...it's nice to hear that you are open minded about how to handle your DD's gifts.
Azuil