You know it is interesting. I built a blue water 45 foot sailboat and finished it in teak. I made all the doors and drawers for that boat and I always glued the panels in. The boat is now almost thirty years old and none of the doors have failed. They still look great. Go Figure.
When I build doors nowadays I glue the panels in. Could it be that most of my panels are plywood?
The suggestion to use ample glue may be OK, but if you get too much glue it is hard to clean up where it leaks out when you clamp. This is OK if your making a new door as a little sanding will take care of the problem. But, on this finished door a bit of glue spread evenly will do as well as a gob of glue. Just be sure to clamp tight while the glue dries and use a good wood glue. If it were me I would use Elmer's wood glue on that Oak.
On my boat I used a two part epoxy glue everywhere, but that may be a little overkill for your RV doors.
