I don't know what the amp draw on that fridge would be...hopefully there's some info about it in your document package or on the manufacturer's web site. I think that the installation of a inverter would work depending on the amp draw. The TV's hot wire should be able to keep the camper's battery(s) charged while towing. Hopefully the camper's power center is located close to the outside kitchen for ease of wiring.
Nights camped in 2013 - 55, 2014 - 105, 2015 - 63