While fixing a bad ground will prevent a earth to trailer shock, it doesn't mean you have fixed the problem. Before you call it "fixed" try plugging into a GFI. A solid ground is an important safety feature, however there had to be something leaking to the trailer frame to make the skin hot. If the leak still exists, and is over 5ma, it will trip a GFI, and should be found & fixed.
One more point. If the trailer is properly wired with no connection between the neutral & ground, reverse polarity will not make the chassis hot. It is still a bad situation to have, because the circuit breakers will no longer protect against a short to ground, but it won't make the chassis hot without a fault.