I'm with Larry.
You are not overloading the circuit, you are tripping the ground fault because of a ground fault.
I found your rig:
https://lakeshore-rv.com/arctic-wolf/265dbh8 This thing is a beast with two furnaces and two AC units...yours may be different.
How to figure out the problem:
First, verify that the interior outlets are (or are not) on the "Gen" breaker. Don't assume. Turn off the "Gen" breaker, plug shore power into the pedestal, double check that the inside GFCI is on (reset, not tripped), and test the outlets. If they work, they are not on the "Gen" breaker. But going forward, for testing and ruling-out purposes, let's assume the inside outlets ARE on the "Gen" breaker.
A GFCI outlet connected to an inside circuit SHOULD be "first in line" on that circuit so it can protect all outlets downstream of it, BUT THE GFCI OUTLET WILL BE DOWNSTREAM of the "Gen" breaker. I assure you, there is a GFCI outlet somewhere in the rig. Trip that inside GFCI and then test the 20 amp GFCI on the pedestal. If it still trips -- which is highly likely, because the
inside GFCI should trip if it senses a fault at that outlet or those downstream of it -- unplug from shore power and chase down all OTHER loads on the "Gen" circuit breaker. Again, it's VERY unlikely to be related to your outlets if the inside GFCI outlet isn't tripped already.
The "Gen" circuit breaker may very well also supply one or several other "appliances." The lug on the breaker may have more than one wire attached to it. Also important to remember, the "Gen" breaker feeds that first interior GFCI outlet with unprotected wire. The inside GFCI is highly unlikely to trip due to a fault in the wire between the breaker panel and the first GFCI. It might, but not guaranteed. So that wire is also suspect.
Other loads on the "Gen" breaker could be anything, but bear in mind that they are not likely to be BIG loads, because you can easily load the interior outlets with 15 amps using a coffee maker, toaster, and so on. Any appliance sharing that circuit is likely to be small. Certainly not the microwave, and probably not a residential or two-way fridge...especially one that also runs on an inverter that demands as much as 8 amps all by itself. I could be wrong on this...but it wouldn't make sense to hang a residential fridge on the same circuit as the interior outlets. But it WOULD make sense for the "Gen" circuit to feed 120 volts to the inverter...more on that below.
From what I can see, you have a big, honkin' residential fridge on a 1000 watt inverter. That inverter on its own can draw 84 AMPS at 12 volts and over 8 amps on 120 volts. Most home fridges enjoy a dedicated circuit. Yours should as well.
The process of elimination may be helpful to rule out some appliances, because some of the circuits may be labeled to identify what they feed. But something on the "Gen" circuit breaker is "leaking voltage" enough to trip the GFCI...but not enough to trip the "Gen" breaker.
Note that your panel breaker is NOT a GFCI, so unless the current leak exceeds its 15 amp rating, it will not trip. This has to do with a voltage leak to ground....not excess current. That's why the GFCI on the pedestal won't tolerate it but the inside breaker will.
Years ago, I found a manufacturer's cabinet screw literally driven through a 14/2 wire in my rig, and then only backed out enough to no longer penetrate the wire. No doubt this was discovered in testing the rig and trouble-shooting the dead short created by the screw. The SOB doing the work was too lazy to remove the screw entirely and to open the wire jacket and add some electrical tape to the black or white wire in the jacket that had been compromised by the screw. Backing out the screw restored the function of the circuit, and so the "technician" left it as is.
Wade in with an open mind and don't be surprised if you discover a staple or screw creating a problem...and that fastener might be coming up through the floor from below...or coming through from outside the cabinet space where the rat's nest of wires is. A screw tip may have chaffed its way through a wire jacket. (I had that with the gravity fill pipe on the same camper I mentioned...after a couple years, I had a big hole in my fill pipe from an errant screw drive by the same SOB no doubt!!)
If you don't see an obvious "screw up", remove the appliance(s) on the "Gen" circuit one at a time and test see if the pedestal outlet is happy, then reconnect to see if any one of them trips the GFCI after restoring its connection.
Why didn't this show up sooner?
If you routinely connect to a 30 or 50 amp outlet on a park pedestal, nothing says those outlets are GFCI protected...MOST LIKELY NOT. I suspect the one on YOUR pedestal is not. So a little ground fault leak won't shut down your rig UNLESS you use a smart adapter between your rig's plug and the pedestal. But that little 20 amp GFCI may have just saved your bacon. It's a "smart" connection rather than a "dumb" connection.
Find and correct this problem. You are almost there, because you've already isolated it to a single circuit INSIDE the rig. There's no problem between the pedestal and the converter and breaker panel...it's all downstream of the "Gen" breaker...a very limited number of options.
A bit more sleuthing and you'll be home free.
P.S. There's nothing to be afraid of when removing the breaker panel...so long as you are disconnected from shore power...with ONE NOTABLE EXCEPTION. That inverter connected to your battery bank and powering the fridge should be treated with respect and turned off. It probably connects to the battery bank with what amounts to welding cable, and a dead short on the 6 volt side will make 84 amps worth of sparks...unpleasant at minimum. And on the 120 volt side, there are, well, 120 volts. Shut this down if there's any chance of getting tangled up in this thing.
Remove the front cover (often 4 brass machine screws) and gently remove converter from the cabinet...usually 4 wood screws. Gently slide out the panel while watching to make sure nothing falls out (e.g. a loose set screw on a breaker allowing a wire to come adrift). Expect a rat's nest, but you need only worry about what's connected to the "Gen" breaker and the associated white and bare wires connected to the bus bar.
Look to ensure that the (usually) bare center conductor wire on the offending circuit is well tied into what might be a bundle of bare wires that might be wire-nutted together, or far more likely the bare wire or white wire on that circuit isn't solidly connected to a straight to a bus bar on the circuit breaker panel. I mention the wire nut scenario, because there's no tellin' with RV assemblers. At any rate, the GFCI won't be happy if these connections aren't tight and secure.
If an appliance seems to be the culprit...say the furnace or something else...you could make absolutely sure by jury-rigging a male plug onto the end of the wire feeding the appliance and plugging it into an extension cord that can reach the 20 amp GFCI on the pedestal. If there is a ground fault in the appliance, it will trip the GFCI. A plug like this is available at any hardware store and is easy to install and use again and again.
https://www.grainger.com/product/4A2...P7A1P:20501231
Given that your residential fridge is tied into a 1000 watt inverter, I'd be surprised if it's not on a dedicated 120 volt shore power circuit, and it's likely (not guaranteed) that the inverter has a built in transfer switch to feed shore power to the fridge when shore power is available and automatically switch to the battery bank when shore power is not available. I could be wrong on this...but that's cheap technology, so I'd be surprised if that isn't the case. Illustration:
https://smile.amazon.com/Aims-PICOGL...4955847&sr=8-9 Not all inverters have transfer switches and not all inverters have conventional AC outlets, but it's possible to have both.
Coming full circle, if the "Gen" breaker feeds the fridge thru the 1000 watt inverter, there are two possible culprits. The inverter may have a ground fault...possibly in the transfer switch or elsewhere...and then the fridge could have a fault. But to complicate things, your fridge should continue running, because as soon as shore power stops, guess what, it's running on the batteries through the inverter.
If that's the case, my bet is that the fridge has a conventional plug that plugs into the inverter at a conventional outlet. If so, pull the plug and connect the fridge to shore power directly and see what happens. If it trips, it's the fridge. If it doesn't, it's the inverter/transfer switch.
If the fridge is "hard wired" to the inverter, you can still disconnect, add your handy male 15 amp plug to the wire going to the fridge and test.
A mind bender for sure, but you are lucky to have stumbled into this due to the kluge connecting to a 20 amp outlet on your pedestal.
Linear Mode
