My factory installed genny is wired like Gdetrailer stated. I have a plug in the shore power cord compartment that I plug my shore cord into when I want genny power or unplug it and run the cord to a power post. The cord stays plug into the genny plug so I don't have to mess with it when I start up the genny and if I'm hooking up at a camp ground I just unplug and run to the power pole. Simple, cheap and worry free.
So in the OP's case I would install a plug in the shore power cord compartment and run a power line to the front of the trailer and a female plug. Then make an extension cord to run from the genny to the female plug on the front of the trailer using the appropriate connectors for both the genny and trailer plug.