All GFCIs have a set of contact terminals labeled “Line” and another set labeled “Load.” The black and the white wire, (hot and neutral) from both the line and the load must be connected to the correct terminals on the GFCI. If, for instance, the hot wire from the line is wired to the “Line” terminal, but the neutral wire from the line is wired to the “Load” terminal, it will confuse the GFCI. The main purpose of the GFCI is to monitor the balance of that circuit between the black and white conductors. Mis-wiring the hot or the neutral at the GFCI may render it inoperable, but not to the point of actually causing it to trip. Nor will it likely trip the circuit breaker for that circuit.
Here's something you can check; be sure the coach is not plugged in and the inverter is off before proceeding. With the GFCI removed from the receptacle box, there should be two sets of Romex conductors located in the make-up box. The black and white wires from each must be kept relevant to each other. In other words, the same pair of black and white conductors must attach to the correct (line or load) terminals on the GFCI. With the motorhome plugged in, the “line” set will be energized; the “load” set is everything else downstream of the GFCI and will not be hot when the GFCI is tripped. There is a remote chance the new GFCI is faulty, but chances are it is simply a case of incorrect wiring. I’ve actually seen all the white wires bundled into one wire nut behind the GFCI; a no-no for GFCI wiring. It is best to have a pro RV service tech take a look if you are unfamiliar with working on a live circuit. I certainly don’t recommend it. The circuit must be energized at a certain point in order to differentiate between the line-hot and the load-not hot sets of wires at the GFCI. I know this may sound a bit confusing, but a pro tech with an accurate VOM will be able to quickly discern the problem with a few simple measurements.