Unless that outlet is only on the main breaker, it should not have been a problem when you "turned off all the breakers."
Perhaps you are pulling too many amps in your trailer. You house outlet is probably on a 15 or 20 amp breaker and if anything else is on that circuit you might be over loading it.
I routinely plug our trailer into a home outlet that is a gfci outlet with no problems and there are two gfci circuits in the travel trailer. I can even run the A/C as long as nothing else is running in the trailer other than the fridge.
First, I would inspect your power cord to the trailer for damage. If it plugs into the trailer, disconnect it from the trailer and plug it in alone. If it is hard wired to the trailer, turn off the main breaker and see if the gfci trips. You could have a bad gfci or the microwave is tripping it.
You need to get an outlet tester
and check your house outlet then check each outlet in the trailer.