Competition is the right word.
My g-daughters competed with their dance classes on local and state levels. Won many and lost many.
It's competition between the parents children get so upset. You can spend a lot of money to and get tears and hurts. I know this sounds hard, but I hate see kids hurt. There is a program on TLC channel call Toddlers and Tiaras just watch that program.
Let your g-daughter know that life is not always fair.