Is the fan you hear the inverter fan or the converter fan? Inverter makes 120V out of 12V
battery juice. Converter turns 120V *into* 12V
I'd check the breaker on the 30A shore power outlet on the home. It's pretty easy to accidentally go over 30A with a 50A trailer ....
We keep a dirt cheap outlet checker plugged into one outlet on our trailer at all times. It quickly tells you if there is 120V in the trailer. We also have a display on the hard wired EMS that tells you if there is 120V on the shore power input. Between them, they make troubleshooting something like this pretty quick ....
If you don't have a setup like this, a couple quick checks with a multimeter will do the same thing. Check at an outlet. Then at the bus bar in the breaker panel, next on the output side of the shore power cord, and finally at the socket on the power post. ( order really doesn't matter, but that's how most folks do it ...).