Thank you everyone for your thoughtful replies. They've all been very helpful as I try to get to the bottom of my confusion.
DD was a real sore loser when she was 2 even though all we were playing were collaborative board games. We've been working on this issue continuously and she has improved quite a bit. On the other hand, with soccer, she couldn't care less if her team won or lost. She hated it so much that she just wanted to be out of there.
I'm all for teaching her to handle competitions in a healthy manner and be gracious about winning and losing. I'm just not so sure if music needs to be involved in that process. On the other hand, she has become a little diva when it comes to music that I think she could use a reality check. It might make her more competitive in the long run but I think it's better for her to realize that she's not the only competent musician under the sun sooner than later (to be fair, she has acknowledged that one other person is a better pianist than she is but he is a seasoned professional jazz pianist).
I'm feeling rather neutral about piano competitions. I will take her to a piano festival this summer to see if she likes the atmosphere. Her teacher has mentioned competitions in passing but she knows piano is DD's secondary instrument and we want her piano journey to be fun and stress-free.
We've only had 2 lessons thus far with her new string teacher but we've been having a lengthy discussion regarding DD's aptitude, curriculum, goals, and potential. I do believe we are on the same page overall but she's a bit more pro-competitions than we are for DD. Anyhow, we are still talking and we seem to be going towards the direction that she'll have DD on a "competition diet" and we'll enter next year (2016) if DD is more predictable than she is now and we should know more after the winter recitals.
Thank you everyone again. I do think she is far too young to be focusing on one activity at the expense of everything else. I need to find a balance without making her feel that we don't respect her own choices and that is a lot easier said than done.
