In your s&b house, the ground is a real earth ground. It is connected to a copper rod driven into the ground or to your water supply pipe. That is what GFCIs are designed to deal with.
The GFCI measures the difference of the currents in the hot and neutral lines. Under fault conditions, some current will flow to ground, possibly through you. This results in less current in the neutral than in the hot, and the GFCI trips
In an RV, a true earth ground is not practical. The ground is often tied to the neutral, but it shouldn't be. That will cause the shore power GFCI to trip. If you have a multimeter, disconnect from shore power and check the resistance between the neutral and ground. It should be either open or at east 1 Mohm.
Retired electronics engineer. Avid paddler & birder.
2011 Silverado 2500HD, diesel, 4x4,crew cab, 8' bed
Palomino Puma 253FBS (27' 5er) & '94 19' Class B