Before going through the work of removing the trim, I would take a hose to narrow down where the leak is coming from. It could be coming from behind the blue trim on the rub-rail (which has rivets all behind it), or from somewhere above that. Start at the bottom & work your way up. First have your floor relatively dry. Place a papertowel on the floor in the area that you have seen dampness. This will show you the water pretty quickly after you start hosing down one area at a time (hold the hose in each area for at least 2 minutes & wait about 5 minutes in between moving positions--it sometimes takes a while for the water to work its way in). When you finally locate the leak, seal it up with either Parbond or Vulkem. You must have the leaky area free of any old remaining sealant before you apply the new. Good luck!! I had about a million leaks on my trailer when I bought it, but they're finally all located & this was my best method.
1964 Bambi II
1988 Avion 32S