Fridge not wanting to start on LP is a common problem, but one that is generally fairly easy to solve. I'm assuming you've already checked to make sure you have propane in your tank(s) and your tank valve is turned on. The LP line is generally a long one, and it will get filled with air when the tank is shut off and the LP line is disconnected. Fastest way to clear the lines of air is to open the door & a couple of windows, then turn on a cook-top burner and light it. Once the lines are cleared of air, the fridge should fire up on the first or second try. If that doesn't work, you'll need to take it to the dealer for a check-up when you return from your trip. (There are quite a few post on this site about kinked propane lines.) You may have to run the fridge on electric mode (auto) for this trip. Get it good and cold, before you leave, and it should stay cold for several hours while traveling if you avoid opening the refer door. You can plug it back in once you get to your campsite.
Hope this helps, and have a safe trip.