Off the road now with more time to write. Some folks seem to have no problems with the 3 button Dometic thermostat--others. me included, have nothing but trouble. Since the thermo sends communication signals, it takes the AC a moment to change fan speeds; so it sounds like it is stopping as it changes speeds. Unfortunately, this appears to be the design of the unit. Pretty poor design IMHO. The other problem which I experienced was that the thermo doesn't seem very accurate. You can tell what temp it thinks it is by turning everything off and then pushing the + or - button.
There were some early faulty thermo/control board problems which I also experienced, that when the unit was switching off from low would cause it to pause for 2 seconds, then switch to high fan, then turn off. the solution for us was to pay to replace the thermo and control board at our own expense. While that solved the screwy turn off problem, it still would not run in low fan continuously. In addition, when the thermo was trying to start the furnace, the control board in the AC would make lots of clicking noises that were so load they would wake up.
For us our problems were solved (we hope) by the second Dometic AC failure in 10 months. When our OEM unit went out a few months out of warranty, Dometic gave us replacement parts but we had to pay the labor. 10 months later the replacement went out. It seems that Dometic has a high failure rate with Chinese manufactured AC units. Being in a time crunch 2 days into a 2 week trip, we opted for a Dometic scratch and dent unit made in Elkhart and a 10 button control. I wanted to switch to Coleman or Atwood but there just wasn't time or parts availability. The 10 button thermostat seems to work way better than the 3 button. It still uses communication signals, but it doesn't have the obnoxious pauses between fan speeds. The speeds just switch. Also, the thermo seems much more accurate in relation to the actual temp. in the trailer. I believe that the 10 button can be installed on any Dometic by a competent shop. But the better solution would be Coleman with a household thermostat.