Check your grounds. If I recall correctly a GFI will not work properly if there is no ground. On both my coaches the 110 ground(s) are solid copper wire run to clamps on the frame. One looked pretty good, the other was quite corroded but cleaned up nicely. One was on the passenger side directly below the breaker panel, the other was on the driver side just ahead of the Onan.

Physically disconnect the water heater element, both the white and the black leads. You probably have a heating element shorting through the water in the tank to the grounded case of the water heater. You can easily disconnect these in the AC breaker box. Make sure you disconnect BOTH the white and black leads, then try the other electrical things again.

On a GFCI the current going out has to equal the current coming back. If you have some type of leakage from a white (neutral) wire to ground some of the current will leak back and not go back through the GFCI and it will trip. If you have a connection between the white wire and ground everything will work correctly when not plugged into a GFCI. However if you do not have the coach properly grounded you could get quite a poke when touching the GMC and standing on the ground. Think grabbing the handle to get in.

So what is most likely happening to your GMC. Many have suggested the water heater element. If the element has gone bad internally near the white wire end it will work, but leak current enough to trip the GFCI. If the failure point was near the black lead (hot) it would blow the fuse. As was stated, if you disconnect both the white and the black leads at the water heater element and now it does not blow the fuse it is the element.

GFCI's protect you against bad wiring or devices that can cause a shock. The problem does not have to be on the hot side of the system.