Do you have 120V power generally in the RV?
Do you have 120V power at the fridge outlets? I would double-check that the GFCI in the RV has not tripped. Both fridge outlets would likely be on the GFCI circuit as the outlets for them are in potentially damp/wet locations. If it has tripped and won't stay reset, it's possible that the GFCI is bad, or that there's some wiring problem, or one of the fridges needs repair due to leaking current to ground.
A 15A outlet should be quite capable of supplying both an RV fridge and a dorm fridge simultaneously. The dorm fridge uses maybe 100-200W running, and the RV fridge about 300W, so you're consuming maybe 5A of the 15A that the supply is rated for. Obviously having other things on the same circuit may alter the situation.