The longer the extension cord, the larger the wires need to be. For a 100' run, 14 ga is a bit small. 12 ga would be better.
A electrical meter that reads mega ohms would tell you where your weak link is. I bet you know someone who has one. The GFI trips when there is a different amount of electricity running through the black wire and the white wire. Unplug the trailer, and put the meter on mega ohm. Put one lead on one of the prongs of the trailer plug and the other lead on the ground prong. see what it reads. Should read very high say 30 mega ohm or more. Then leaving the one lead on the ground, move the other lead to the third prong and see what it says. If you get a low reading during either test, you can go inside and turn off the breakers one at a time and recheck. When your reading goes up, you found the circuit the problem is on. You could also check each appliance with that meter.
Without a meter, you could shut off all the 120 volt breakers in your 5th wheel and then turn them on one at a time, see if the GFI trips. The problem is if you have two or more minor problems on different circuits they could be adding up to enough to make the trip happen. Turn off all the 120 breakers except the one that feeds the heater.