GFCI's work by comparing the current in the hot wire to the current in the neutral wire. If there is an imbalance, in the order of a few milliamps, the GFCI will trip. The GFCI assumes the imbalance is caused by current leakage to another path, such as to the ground connector or through a body to ground.
In a RV, a common source of this leakage current is the 12 volt convertor, especially the "newer" (post 1980-1990 era) switching type power supplies. These type of convertors commonly have input RFI suppression to keep high frequency energy off the incoming power wiring. These filters typically leak several milliamps to ground as there normal function. As they age, the leakage current can increase (that's why a GFCI might not trip when the RV or converter is new, then after a period of time the GFCI starts to trip). This leakage current can be high enough to trip a GFCI on the shore power.
Also, using more than one GFCI's in series can cause nuisance trips. The normal operation of the sensing circuitry in the GFCI can cause an apparent current leakage in an upstream GFCI. Again, as the GFCI ages, this apparent leakage current can increase. This can occur in a sticks and bricks house as well as in a RV.
Rick & Debbie; Brandy & Schnoodle Dexter & Fritz R.I.P. the Doxie "Kids"
2015 Jayco Pinnacle 36RSQS 5'er
2013 Chevy Silverado 3500HD LTZ, 6.6L Diesel Dually; B&W Goose Neck and Companion 5'er hitch