Mine has a house-style door lock but no deadbolt. It should be easy to replace- I tried for about two minutes one day and could not get the knob off- it has that style of knob where you have to remove an outer sleeve to get to the screws, and I couldn't quickly get it loose. Then I forgot about it. A deadbolt would probably be more secure so I'll look and see if that would be do-able.
I had the same problem with my campster
. I replaced the striker plate on the jamb and it helped a little. It turned out the door in the area of the door knob was very weak and flexible. I strengthened the door, about 12 inches above and below the door knob, by removing the door knob and clamping 1X4 boards to each side of the door to eliminate outward expansion and very carefully injected the triple expanding foam you can get at stores such as Home Depot. If you put to much in at one time it will warp your door so you must do it in small layers.