there is NO proper reason for an RV absorption fridge to have to have a 'converter' plugged in, even for 120v operation
it does use 12v control circuit, but if the battery is charged
it should work on 120v or LP with a 'converter' unplugged
there is a cross circuit short or back-feed someplace
do you have a 50amp RV plugged into 50amp service with an open neutral or open hot leg
converter is offline
beg borrow or BUY a 30amp or larger battery charger
use an extension cord to the power pedestal, and connect the charger to your battery
set your fridge to LP, at least you will have lights and your fridge will stay working
while you trouble shoot your problems