Are you replacing trim that was on the wall or part of the trailer's framing?
I guess you could use 5200 adhesive (usable surfaces should be on the label) but it's fairly pricey for attaching wood. Are you hammer-challenged?
The insulation in the floor has the function of any insulation product, it helps keep the inside warm or cool.
Edit: Just remembered you were the guy with the "floating shell". You are probably referring to the bottom sill of the wall framing with "boards". Now I get it.
No, you can't glue the wall back together. You need a bunch of mechanical fasteners in there, nails or screws. If you haven't already done it, you'll need to expose the wall cavity where you can drive the fasteners in. The fasteners should attach studs in wall to bottom sill and bottom sill to trailer floor. In some trailers, the floor is then bolted to the trailer frame. In some, the bottom sill with floor is through-bolted to the frame.