Determine the time that the DW is most apt to dry her hair. Put the fridge on a timer that turns it off for a 2 hour period during the hair drying period. The only problem will be that it will be a PITA to reset the timer, every time that you interupt AC power.
EDIT. Powering the outside fridge off of a non-GFCI circuit or extension cord is probably a violation of code. If you don't care about code, just replace the GFCI with a regular plug. Homes with electricity, were built without GFCIs fot for over 60 years.