Using a continuity meter, I would first confirm (with camper unplugged from shore) that there exist NO continuity between neutrals and grounds at campers main panel, meaning, no undesirable ‘eddy currents’ causing the shore GFI tripping…
Note however, that IF you have an onboard genny or inverter, bonding of neutral to ground may be happening passively at either device via a ‘floating ground’…
Outside of that, it could be a defective leakage within the hot water heater or refer (an electrode element, neutral to ground affair…), or (since it is a new rig) more likely, it could simply be that this fussy home GFI is ‘daisy chained’ (to save builder moola) into far too many receptacles - try dedicating this home GFI circuit to strictly just the camper by temporarily UNPLUGGING all relevant home appliances on that particular GFI circuit, then try again..
3 tons