I am sure there are many different ways to fix this problem. Yes, there is a piece of wood inside the trailer, but it is covered over by a piece of curved fiberglass that is then covered by your ensolite insulation. My solution to this problem was to take the door completely off (it's actually fairly light), I drilled out all the old screw holes to a 1/2 " diameter size. I only drilled far enough to go through the wood and not into the fiberglass curved piece inside. Then I took some 1/2" hardwood dowel, cut them to length, and 'glued' them into the holes using marine epoxy. Waited 24 hours for complete drying and then pre-drilled new 1/8 " guide holes for the new STAINLESS #10 by 1 inch screws I used(screws may have been longer - I just used the same length as the old originals which I believe were 2 different lengths - 1 for the door side and one on the trailer side). Door is now awesome. Actually did this to all the holes including the ones in the door. The hinge hides 95% of the wood dowels. (my trailer is colonial white(I call it yellow) and Canadian Tire sells a spray paint
that is a Recreational White that is really close - used it to touch up))
Just in case you don't know, the door will never (NEVER EVER) line up 100%. You can get it right on the hinge side of the door but then the 'belly band' ridge is way off on the other side. This is normal as there was a problem with the moulds when these trailers were made.
These are just the general guide lines of what I did. Important things are to use new screws that are stainless and the right type (countersunk head) so that they don't interfere with the hinge pin. Use a marine grade epoxy as it can stand the weather (bought mine at Home Depot. Dual squeeze tube that you mix). I let the rotted wood in the door and trailer dry for a day after drilling as the wood was still too damp for epoxy. I put the top hinge basically exactly where it used to be but moved the bottom hinge, where it attaches to the trailer, slightly to the left to compensate for door sag and hinge wear.