I don't think I'm smart enough to tell whats actually going on not being there and armed with my old fashioned less sensitive Simpson 260 ANALOG meter, so I will throw out a few thoughts:
1) Typically those small portable gensets would have the Neutral bonded to the metal case/frame and likewise the receptacles 3rd wire Equipment Grounding Conductor terminal is bonded to case/frame and Neutral. Thats the single point Ground. On a cheap unit I could imagine all that taking place in the receptacle outlet and that's a place a wire could be broke or missing ???
2) As far as Hot and Neutral being reversed, are you sure when you wired that breaker box the Neutral wired to the Neutral Buss and the Hot went to the circuit breaker?? With the setup you have I'm unsure if that "tester" can actually determine Hot and Neutral reversal??? But no warranty on that I just don't know the tester and how youre actually wired.
3) Typically an RV panel does NOT have Neutral bonded to Equipment Ground (like in a home entrance panel). The Neutral Buss is insulated and isolated off the case and Equipment Ground. That means if you ran a Hot and a Neutral and the 3rd wire Green/Bare equipment Ground to that RV panel, black Hot to breaker and white Neutral to the insulated stand alone Neutral Buss and the Green/Bare Equipment Grounding to the Ground Buss.
4) I dont think driving an earth ground rod will cure your problem. Heres the deal, its permissible to power plug and cord connected equipment from that genset provided the tool/appliance is plugged into on board mounted receptacles NO GROUND ROD REQUIRED.
HOWEVER if youre running the genset to a home breaker box and out of the box to feed loads (like AC etc) THEN THE GENSET NEEDS A GROUNDING ELECTRODE and it attaches to where the Neutral bonds to the case frame and the equipment Grounding Conductor.
PURE GUESSES AS TO WHATS GOING ON
Perhaps the Gennys Neutral is NOT connected to the case/frame or the 3rd wire equipment Grounding terminal. Id really look at that!!!!
Perhaps the RV panel is mis wired or Neutral and Ground are mixed up
If Neutral isn't connected to case frame and you have a sensitive high impedance digital meter its no telling what youre reading as voltage gets induced into parallel conductors.
Id insure the gennys wiring,,,,,,,,, its Neutral to case/frame and ground are bonded,,,,,,,,the RV panel is wired correct,,,,,,,,,,install a ground rod at the genset,,,,,,,,,,,,,try an analog meter and take some readings
Best I have to offer not being there
Im headed to Wisconsin later today in the RV and may or may not be back online so much the next week so yall take care and behave yourselves lol
John T