As said above a GFCI compares current between the hot and neutral... In this case at the receptacle in the garage. The OP said with a "cheater" adapter in place (ground lug cut off) the GFCI doesn't trip, so, the leakage is from the neutral to ground. Removing the neutral from the converter at the RV panel also prevents the GFCI from tripping.
(After further thought it could be a hot to ground fault... But that would normally trip any breaker)
1). Observe the neutral bus bar in the RV panel. All of the neutrals should connect to one bus bar (white wires) observe the ground bus bar(the bare conductors) these should be on a separate bus bar. If there are any crossed wires (whites and bare conductors) this will trip the GFCI.
2). Turn off the breaker supplying the converter... If the GFCI still trips with other loads running the fault is N-G in the wire or converter.
Try these tests and let us know the results and we can isolate the culprit.
Joe