The alternator will make plenty of power for the fridge.
The problem is the wiring. Your camper charge wire, through the 7-way RV plug, is only 12-gauge at the largest.
The way to get enough power to the camper for running loads like a refrigerator or charging batteries a whole lot faster is to run a separate, large gauge charging wire.
Sometimes I do this simply by buying a set of 25’, 2-gauge jumper cables and cutting the clamps off.
Put lug terminals on and connect to your truck battery, run it to the trailer.
Use an Anderson connector, it’ll handle 100 amps.
Run similar cable to your camper batteries.
It’s not a bad idea to put a 100-amp circuit breaker at the beginning of the cable near the truck battery.
Getting DC power across wires at low voltage is all about wire size.
Bigger is better.