Couple of things that I would recommend here before switching the thermostat out. The first thing to do is to switch the AC unit to the quick cool option by dumping the A/C into the main room where it is located vs. the vent system by opening the slide mechanism on the AC from the inside. If you can get a temp reading from the air coming out, check and see what the difference is between it and the outside air temp (you might just be able to check this by feel to see if it is cold or not).
This will give you an idea as to if your AC is working properly or not. If the AC coming out of the quick cool is cold, but the AC coming through the vent system is not, you might just have a leak throughout your vent system somewhere (probably caused by gaps where the holes were cut for the vents in the ceiling, where the vent system connects into the AC system, or both.) If you have leaks, the cold air is probably escaping into the roof itself rather than going into the camper and you will need to seal this up to fix the problem, or have a dealer do it.
I had a similar problem with my last camper and after going through the process in this thread, it was a night and day difference. I documented as much as possible here and it is really not that bad to check and correct if this is the problem.
Second air conditioner