Well I agree with others that something caused a dead short. Here's what I would do. I would fix only the obvious essentials at first because I'd want to know for sure where the fault was.
Buy a fuse holder and 30 amp fuses at the auto parts store. Cut the positive wire to the destroyed breakaway switch because it's an obvious fault. The pinched wire underneath may look suspect but I would leave it alone for now.
Wire a new battery to the positive terminal on the trailer using the 30 amp fuse first at the positive terminal of the battery. In other words make sure that all the electricity for the trailer goes through the 30 amp fuse first before it goes to the trailer. Do not connect the negative terminal at this time.
I would not connect the negative because if there is a short, yes the fuse will blow but it will also cause a spark by the battery. So I would make a big temporary test switch like this.
Get a set of jumper cables. On one end of the cables hook the red clamp to the negative post of the battery and hook the black clamp to a good frame ground. Scrape some paint off the frame is you have to or clamp to a clean bolt.
Grab the other ends of the cables and back up a few feet. When you are ready to connect power to the battery just clamp the red and black clamps together. By doing it this way if there is a big spark it will be where you made the final connection and not right up by the battery where it could cause an explosion.
If the fuse does not blow start wiggling wires on the tongue and under the trailer and see if you can get it to blow.
If the fuse blows immediately disconnect the red and black clamps in your hands and replace the fuse.
Fix one or all of the suspect things you found already and then go hook the jumper cables together again. If the fuse stays good then you have most likely found and fixed your problem. If the fuse blows again then you'll have to keep looking.
