The electrical wiring is run behind the interior skins, so there is no way to replace all the wiring without tearing the trailer completely apart, unless you want it to look like some kind of hack job with conduits running all over the place and protruding electrical boxes sticking out of the walls.
The way these trailers were wired, is sort of a "spine and ribs" configuration, where a big bundle of wires runs the length of the trailer in the center of the ceiling, and then where an outlet is needed, a branch is dropped down to it through the walls. Since the wires cut through the metal hoops/ribs that hold the trailer in shape, it would be really hard to fish wires into place (or even to remove the old ones, as they are usually anchored to the shell).
But I would start by getting an electrician out to your trailer to actually troubleshoot what is happening. It could be you have a single outlet that is shorting to ground and causing you a lot of trouble, or maybe someone has installed a light fixture on the ceiling, and unwittingly put a screw right into the wiring bundle. The fact that things are melting instead of popping fuses may suggest that a previous owner has done some wacky stuff with the fuse box. Fixing the problem would be a lot easier than rewiring the whole trailer though.
The AC current distribution is done pretty much just like it is done in a house. Having an RV tech come out may be helpful, as he should have a clue as to how they are wired, and the subtle differences between an RV and a house, but in a pinch, a regular household electrician ought to be able to sort you out.