My guess from your description:
1) Heat Load. By not opening a roof vent to let the hot air escape as the trailer filled with cold air (which sinks) you forced the air conditioner to try and remove ALL of the btus of heat in the camper. This will cause continuous operation of the compressor which, like any motor, will eventually will over heat and shut down. This is bad for the air conditioner's health.
2) Humidity. The air conditioner cools by two primary methods (in effect) by lowering the air temperature and removing humidity. Of the two, removing humidity is the most effective in you "feeling" cool. You will "feel" cooler in 80 degree air at 60% humidity, than in 80 degree air at 98% humidity.
To remove humidity, the air conditioner MUST cycle. Shut off and let the coils warm up so frost and ice formed during the ON cycle can melt and be removed via the roof drain. By setting the thermostat at 70 with an outside air temp at 80, you were doing a "good thing."
BUT, the air conditioner never got to see that outside 80 degree air because it was working with 104 degree air; see the importance of lowering the heat load?
3) Ice detector probe. There is supposed to be an ice detector probe in the cooling coils to protect the compressor. The probe detects icing and will shut the compressor down to clear it. The fan motor still runs but the compressor does not while the coil tries to warm up. Depending on how fast the ice accreted (built up), this could take a long time during which no cooling and low, or NO, air flow is coming out of the air conditioner regardless of fan setting.
4) Short Cycling (start up then shutdown in a few seconds) has several possible causes.
4a) Voltage is one. 15K BTU air conditioners draw many more start up amps than the 13.5K variety. If you are running the AC off of a small diameter extension cord for example (or low voltage at the source from a heavily tasked campground), the start up amps required can exceed the ability of the motor's internal thermal protection to handle. It can open and shut down the compressor well before 20 amp circuit breaker can heat up enough to open.
4b) An air leak between the intake and the forced air outlet sides of the air handler section. Note the metal tape in the frost sensor picture. If the leak allows a significant amount of hot air to bypass the coils, the frost detector will "think" the coils are frozen and will shut the compressor down. It will "immediately" reset (few seconds) and try to restart the compressor. HOWEVER, the compressor will still have liquid refrigerant returning to the compressor; causing rotor lock (and again with the thermal switch in the compressor motor).
In the photo you can see my 15K BTU Coleman Mach III. The "Running Amps" is 11.9 BUT the locked rotor amps is 58 and THAT is at 115 volts.
Yes, if the thermal switch "hangs in there" long enough the 20 amp circuit breaker will open but the compressor should have shut down long before enough heat occurred in the circuit breaker to open it.
As volts go down, AMPS go UP with an inductive motor like a compressor.
5) I have seen cases where that probe has fallen out of the coils (or was never inserted or the coils were extremely dirty from running without a filter) and caused the coils to look like a solid block of ice. The only cure is to let the unit sit OFF for several hours and put a pail under it because there will be water in the camper as the ice melts from the outside, in and the drip pan under the coils will be frozen).
Cleaning the coils on your air conditioners should be a regular maintenance item. AC-Safe Air Conditioner Coil Foaming Cleaner-AC-920 - The Home Depot