V.C.
The hats just may be making her too warm. We lived in GA when my 2 dd's were 2 & 4 .. I never had hats on them .. too hot. I used the spray sunscreen and limited time outside between 10 - 2 (when the sun is strongest - it was too hot to go outside most summer days anyway!) If you're dd is very fair you might want to just slather her with sunscreen and let her go hatless ...