There should be a breaker panel/fuse panel and possibly a built in converter under it.
First, there's two power systems: 120VAC (house power), and 12VDC (car power.)
There should be a battery on the trailer providing 12VDC. That will run lights, furnace, WH/refr circuit boards, slide out motors, landing gear motors, and anything 12VDC of course.
Few things are 120VAC; air conditioner, refr heating element, WH element, microwave and, most importantly, the converter. That will change 120VAC to 12VDC and will supply power to 12VDC appliances and charge the battery at the same time.
So, when you have no 120VAC connected, are you still hooked up to the truck using it's charge line? I find it hard to believe that only those two things work and nothing else does.