But a Tilley hat! They are the best for the Florida (or anywhere) sun - great brims to protect head and neck, cools you off just by putting it on, straps for wind, latest designs have airflo holes for venting. My whole family brings one each when we travel to WDW. Should you or kids still get overheated, you can fill brim with a bit of water to douse your head for immediate cooling.
I'd highly recommend these hats. This is the one I currently wear.
Tilley Endurables - The Finest Hats and Travel Clothing in the World