I had cooling problems with my brand new Dometic for the first several months; I finally took it to the service center. They bypassed the thermostat for testing and told me to record the inside temperature every 6 hours or so for several days and get back to them.
It never did get close to freezing and several times it was in the high fifties. They replaced the entire unit and the new one has worked perfectly for over four years now.
I run it on LP all of the time unless I’m at home cooling it down before a trip, then it’s on AC. It can always maintain a temperature below forty degrees, even in daytime temps in the nineties.