OK, so the GFCI is tripping. It's probably not the GFCI itself that's bad, since more than one are doing the same thing; so you have a problem in the RV wiring. A portable generator works fine because (most) are not equipped with a GFCI.
You have a ground fault of some sort in the RV. One common cause is a bit of water getting in to the outside outlet, or some other semi-exposed AC wiring (such as the fridge compartment). There are other possible causes, too.
Basically, there are two things that cause a GFCI to trip. One is when there's any leakage of current--that is, when the current going in the hot wire is different from the current coming back the neutral wire. A small leakage to ground somewhere causes this situation; and or wet wire connections can allow that leakage through the water. It could also be a fault in some device or appliance; water heater and RV fridge heating elements are common culprits for that.
The other thing that causes GFCIs to trip is a short between neutral and ground, even if there's no current imbalance. That would be due to a wiring problem: a ground wire in the RV electric panel that touches the neutral bus bar, a staple through an AC wire, a pinched or chafed wire....
You may be able to track down where the fault lies by selectively turning breakers in the RV off; if one breaker being turned on causes the GFI to trip, whatever is causing it would be somewhere in that particular circuit. This won't help isolate a neutral to ground fault, since the breaker doesn't cut off either of those wires.
Note that a GFCI in itself is not a fuse or circuit breaker, and doesn't trip due to excess current/power usage. (A GFCI breaker in a breaker panel does, since it's a dual-function device: a circuit breaker and a GFCI.)