Hunter:

Place the inverter someplace where it will not get splashed with water as this will kill it quickly.

Run the 115 vac power to the rear of the vehicle along one of the frame rails using either a contractor extension cord (heavy duty stuff) or exterior rated house cable, and use a lot of cable ties to prevent chafe of the cable.

At the rear end, install a weatherproof power outlet box .

Make up an extension cord appropriate for the trailer that can get to your shore power lead and build a connection adapter there. This should work the fridge underway. Be sure any other AC loads are off, or within the rating of the inverter.

Hope this helps! Have a safe trip.

Doug