GFCIs trip when there is an imbalance between the hot & neutral current. This usually happens when there is a fault (connection) to ground. While GFCIs do go bad, it is far more likely there is a problem with the wiring to or within the trailer. Typical faults are moisture in a receptacle or adapter, a ground fault in the refer heater or hot water heater (if you have an electric element in the water heater) or an appliance in the RV.
If the fault is between the neutral & ground, shutting off circuit breakers won't help identify the problem - a neutral/ground fault will trip a GFCI even with all breakers off.
I have a post that describes trouble shooting techniques
here.
Do take the time to find the problem. The reason everything works when plugged into a 30 amp receptacle is because the 30 amp receptacle doesn't have ground fault protection. A ground fault can make the chassis of the RV live if there is a failure of the RV's ground connection,