Probably repeating others...too many posts to read all of them.
Breakers can fool you. They may appear to be on even when they are tripped. You must fully turn off the breaker before you can reset it.
Harmless exercise that may prove useful. Turn ALL breakers off then back on again. Then press reset on the GFCI. That may solve your problem.
It's EXTRAORDINARILY unlikely that there's some other panel or some other in-line fusing. But there is one possibility. If some num-nutz at the factory installed TWO GFCIs, except in the largest rigs (with two breakers for the outlets), they will be in series on a single circuit.
For giggles, check all outlets to verify that there is only ONE GFCI in the rig. If there are two on a single circuit, you'll pull your hair out dealing with this nonsense. You should replace the second one in line with a regular outlet.
If there are two, trip one and see what happens at the other. One GFCI should be first in line and protect the entire circuit. If you trip the one that's second in line, the first may remain live. If you trip the first, then the entire circuit will be dead. Replace the one that's second in line with a standard duplex outlet.
Bear in mind that the act of tripping #2 may also trip #1, so this is not an entirely foolproof tactic. If both trip, reset the one you think is first in line and check for voltage. No voltage suggests it's second in line. Trip it, and reset the other and see if you have voltage at that one.
If, for absolutely certain, there are two GFCI's on a single circuit, you may need to trace the wire from the panel to the first GFCI. Either way, if there are two, you may go nuts until you replace #2 with a regular outlet.
If all that fails, disconnect from shore power and disconnect the battery. Pull the breaker panel (converter) and check the connections at the back of the panel. Loose screws are not uncommon. If all that's good, go to the GFCI outlet and make sure it's connected properly. There's a chance that one or several wires have come adrift. While you're in the back of the panel, check and tighten EVERYTHING. Loose connections cause voltage drops and eat power and damage sensitive appliances. If the your rig was wired at 4 PM on a Friday, that would explain a lot.
P.S. on this: if the wires to the back of the GFCI are just pushed into holes, make sure there's a connection. It may appear to be pushed in, but if you tug on it, it may come out. If the wire wasn't stripped back far enough, there may be no connection. Screws are better.
And let's not forget the possibility of a faulty GFCI or faulty breaker. While you're checking the wiring, make sure everything is safe and plug into shore power. Use your multimeter to check for voltage at the back of the breaker and at the input to the GFCI. Be sure to unplug from shore power before trying to do repairs. If you have voltage coming into the GFCI, but no ability to activate the GFCI, replace it. It may be a dud. Buy a replacement at the hardware store and install it.
Should you have to do this? Of course not. But all of this will take you less than an hour or so and a few bucks, and that problem needs to be somewhere. You must simply be persistent to find it.
Going back to the beginning and checking breakers. If you reset a breaker and it pops right away, you may have a dead short from some moron driving a screw through you house wire. I found this in my previous PUP. The screw was driven into the wire and then backed out again. Doh!!
As they say, s_ _t happens.