From what I gather with a web search one of those three wires is used to digitally communicate with a control box somewhere else like the AC unit. So basically it's a much different system than most and I haven't found anyone that could easily make other thermostats work with it.
Here is a google search on the subject - https://www.google.com/search?q=dometic+thermostat+3+wire+communication

Thank you for the link. I followed what that person did to get the Nest thermostat to work.
He copied the digital signals and used a nano rdunio which is a simple computer. Ardunio are often used for robotics. The high low state is used to trigger relay switches, That translates into digital signals.
All he accomplished was getting a thermostat with WiFi access. The controller at the a/c is still doing the same thing it was with the other thermostat.
Making a 12 vdc to 28 vac is not hard to do. Replacing the a/c controller like the Ardunio would be required to use a home thermostat.

A couple of years ago our thermostat was giving up the ghost. We were in Arizona and went to a local RV parts supply where the fellow took all the make, model and other information to contact Dometic. It was going to cost over $300 for whatever was necessary to connect with the ac and the furnace and upgrade to a newer thermostat. By chance someone posted a question regarding the same thermostat we have, in a FB RV group and the answer was to spray the dirty connections with electrical spray. This person also had the cover removed, which was something we hadn’t been able to figure out without breaking it. The spray fixed the problem so we no longer need to attempt to upgrade old equipment.

You might consider a Micro-Air Easy Touch RV Thermostat .....
https://www.microair.net/products/easytouch-rv-thermostat?variant=32199143555156

Those Dometic thermostats are not very good and I never could get one to work right in my unit. And I know many others that have the same issues. Unfortunately they are not replaceable with a standard thermostat since they communicate digitally to the control board in the AC unit. There's a workaround where you use the Dometic as an A/D converter and use a standard thermostat. I tried that and it works but it's complicated.

I eventually went with the EasyTouch RV thermostat and it's much nicer and works great. A little pricey but they are the only ones out there that have a replacement product for the Dometic.

As the EasyTouch guy told me they are thankful every day for Dometics lousy engineering. It's what keeps them in business!

The current thermostat has only 3 wires red, white, orange. The red is probably 12+ — Randy Williamson

My Dometic came with red= +12v, white= GND, green= COMMS

Dometic

EasyTouch RV thermostat and it's much nicer and works great. A little pricey — Steve Lawhead

WOW.... was it ever pricey. Shipping across the border was $$$ but sure is a nice thermostat

Thank you