The following may work although it has not been tested.
Try downloading dpClothing+ (1.0.3) Clothing Variations and Toggles (Gloves, Vest, Top, Hair, Bag and more) Once you have added it into your server, get inside the vehicle use the default ( Y ) to pull up the GUI, Or alternatively use the following command /hat
This may or may not allow you to have it on inside the vehicle you’ll have to test it out. I do not believe that there is a script that is just for allowing you to keep hat on inside of a vehicle at this time.