The issue with replacing the dometic 3 wire thermostats (that cover both heat and A/C anyway) is you need to run new wiring. The 3 wires are proprietary to a control box that is the full themostat wiring (see attached photo). The communication between them is digital on 1 wire (canbus) and +/- wires for the other 2. So you are either stuck with the 3wire dometic thermostat lineup or you have to find the box and run new wiring for a 4 or more likely 6 wire thermostat depending on how many AC units, heat pump or zones you may have. The conversion box is usually inside the ac unit or near the furnace.
If you are not an hvac person I would not suggest trying to replace this on your own as you will need to understand voltage differnces (most thermostats are 24v not 12v) and how various thermoststs work and it may require several relays if using a 24v thermostat to not fry any of the AC or furnace control boards.
To be fair the dometic UI is not the greatest and many people are confused by it which is why people complain about the A/C fan running when running the heat etc. If you review the manual (get good at the reset command) you will understand why it is doing what it is doing usually.
Hope that helps. If you decide to swap it out be sure and take lots of pictures to help anyone else willing to take the project on.