Okay....I am wrong... I DO NOT have an invertor....only a converter ( I think...? ) No AC power from batteries... only DC from AC....
Now any ideas on where to start...??
Step 1, Turn off and/or unplug EVERYTHING, Set all breakers in the MH/Trailer to OFF, does it trip the GCFI?
NOTE: if possible unplug the 110 to 12 volt converter. If the GCFI holds plug in a lamp and activate the breaker that controls it. If the GCFI holds you are in business for diagnosis, one at a time bring up all the breakers, if the lamp goes out, shoot that circuit, it's deffective, I do not expect the lamp to go out at this step however,
I should add here, I'm going way overboard and checking things most likely not bad, but when shooting trouble that may well be hidden in a wall... You do all the easy steps even if they are guarenteed to not help
Now plug things in,,, starting with the converter/inverter. if/when the lamp goes out shout EUREKA for you have found it
Next turn things on... Again if the lamp goes out,,, Shout EUREKA for you have found it
Many trailers however have ground (Green) and nuteral (White) hooked together, this will trip a GCFI. There is nothing technically wrong with doing it this way so long as you don't get a backwards wired cord (I had that problem with my old trailer, the previous owner had home brewed an adapter for the power inlet, he'd wired the black wire to the shiney screw and the white wire to the copper screw. That trailer would knock you on your .... You know what,,, if you used a commericial extension cord to power it, Using his cord (of course) no problem since he'd wired it the same way. I fixed both of them. I'm cross trained electronics/electrical, In Electronics black is ground, Same for automotive electrical (how he was trained) but in 120/240 vac black is HOT white is not, and green is ground, or at least that is the standard (White is grounded at the breaker box)
You may also have green and white connected together at the breaker box
If the problem is "internal" (not something plugged in) I'd strongly suggest a professional to fix it