I read through your descriptions, and see the following clues.
1. Your trailer is plugged in to a GFI receptacle at the house.
2. You then washed the trailer.
3. Plug in; surge protector analyzes the house power, then engergizes the trailer;
4. Then house GFI trips.
Most reasonable conclusion, based on what GFI's are designed to detect, is that there is a water-path somewhere in or on your trailer that lets electricity go from the 120V circuit go to ground. It only takes the tiniest amount of current.
I would turn off all of your trailer breakers, then plug in to house power and see if the GFI stays on after the surge protector analyzes and allows power flow. If so, then you can turn on breakers one-at-a-time until the GFI trips. That will be the circuit to examine for water (probably where water under pressure could be forced into some terminals; E.G. plug socket, or light fixture.)
Or let the trailer dry for a day, and see what happens.
Don & Teresa
2015 17A: 2011 Honda Pilot