Forgot to mention the reason her hat doesn't stay without being tied on - my girls are biracial and have massive curly hair. So winter hats literally pop off their heads. I use a winter head band for my older daughter, but my younger refuses to even put it on her head.
I know she has a strong minded personality and I don't let her get away with it mostly (pick my battles). I try my best to ignore her temper tantrums when they happen, but also try to plan in advance to try to avoid them from happening. I truly hope it is something she will grow out of.
Sometimes I wish she wasn't so sensitive, but other times am glad she doesn't let snot just run all over her face! Lol