Without putting an amp meter on the power cord, it is difficult to determine what, if anything is wrong. If you have the electric option on the water heater, and your battery is low, you may draw more than 15 amps (what many home circuits are breakers at). Try turning off the electric switch on the water heater (under the outside cover) and see if this makes a difference.
Running any high wattage appliances such as the air conditioner, a toaster oven, microwave, etc can cause the same problem, particularly if you try to run more than one at a time. The campground connection usually is a 30 amp receptacle, twice that of most home receptacles so you may not have a problem when in a campground.
There is an inexpensive device called a Kill A Watt
meter that you plug between the house receptacle & the extension cord that will tell you what current is being drawn by the trailer (among many other things). Worth having if you don't have a clamp on multi meter & know how to use it.
As rubicon327 mentioned in post #2, if it is the GFCI function of a receptacle or circuit breaker that is tripping, you do have a problem with the trailer that should be found & fixed. Since most campground 30 amp receptacles do not have GFCI protection, a fault that trips a home GFCI wouldn't cause a trip in a campground.