Check the power coming out of the pedestal or garage and make sure the hot neutral reverse is not all the way back there. It would suck to chase a problem in the trailer and have it be in the shore power outlet or cord.
Your breaker panel should be real close to where the shore power cord comes in. Unplug the trailer and pull the cover off the breaker box. Make sure the black wires are going to the breakers and the white wires are going to a bus bar. If you can take and post picture of the inside of the breaker box it might allow people on here to give you some more suggestions.