I took my brother's toy back from my cousin
Did your cousin steal it? Why did you need to take it back?
Because I care about my brother.
If your cousin was being unkind to your brother and stealing his toys, it is kind of you to stand up from your brother and get his toy back for him. It would be good to redirect your cousin and help him understand he shouldn't take your brother's things as well.
I'm using my family as an excuse to compete with my cousin.
What you did for your brother was commendable, but it is not okay nor healthy to have a constant competition with your family member or your cousin. I think it is better for you to compete in class or in tournament in sports, rather than having competition with your cousin as it can be seen as petty.