Inverter/charger problem
An 'Inverter' converts 12v DC (battery) to 115v AC. As such, what your trailer is plugged into makes no differance in its operation (or should not).
Where is this '30 amp input circuit breaker' which keeps tripping? If it is a 1500 watt inverter, than it will require up to or even over 125 amps @ 12 volts (allowing for losses in the circuitry) to provide 1500 watts of 120 AC.
Also, 1500 watts is probably the maximum it can put out. If anything else is plugged in to the inverter, or the toaster or the hair dryer takes more than 1500 watts, then it should be shutting down. And many microwaves take over 1000 watts to run and perhaps have a 'start up' requirement of even more; again a valid case where it should shut down.