Charging the camper battery when driving

I also agree that the 12 volt option for powering your frig may not be the best solution. Assuming the heater element in the frig requires 240 watts to cool the box, that translates to about 20 amps. It’s not likely any existing wiring to the back of the tow vehicle is sized adequately to carry 20 amps. Further assuming you use 60 feet of #10 wire for the 20 amp load, the voltage drop in the wire would be about 1.2 volts. The wiring connections could easily result in another 1 or 2 volts drop. So, if you run the wiring directly from the battery, or to a terminal near the battery with #10 wiring, and the battery was charging at 14 volts, you will only have about 11 volts at the trailer battery, or less if the battery is discharged and drawing even more current. A diode would result in another .6 volts drop, so a relay that cut in the line to the trailer would be a better choice than a diode, but the other voltgae drop is still present.
To make a long story short, the idea of running the frig from the tow vehicle 12 volt system doesn’t bode well for success.