The Dometic Cool Kat factory installed unit in my RV sort of acts the same way as you describe. I finally discovered that it was coming on in the last mode it was in when the thermostat called for a change because of a small deviation from the set point. However I discovered, quite by accident, that when the deviation from set point was large, the unit would go into the correct mode. At that point I could set the thermostat to the desired temperature and the unit would work correctly cycling on and off as needed provided it didn't need to "reverse direction".