If you have a breaker type GFI, then it may be effected by many things.
In our case, someone had installed additional outlets in the outside of the coach, but instead of connecting to a breaker they connected the hot to one line side of the main breakers, the safety ground and neutral were both connected to the neutral buss.
With the coach having 50 amp service it could be bad, this was discovered while investigating an AC project by accident.
So, what you may have is something on the 12 volt system that has a return or ground connection that is common with a ground connection on the GFI.
First look for non-factory things and see how they are wired.
Next, plug a radio in the GFI and crank it up, next turn on one and only one thing at a time, when radio stops make note, leave that off and continue until everything checked.
Now check the wiring of the devices that cause the issue, you may have something where they used the ground for the 120 volt device to ground the 12 volt device, this causes a measurable current in the safety ground which creates a difference in currents between the line,neutral and safety ground for the GFI which is what causes it to trip.
Tony & Lori
1989 Country Coach Savannah SE