Most home thermostats require 24V AC to operate. If you are going to use a home thermostat, be sure it has its own battery.
A second problem is some Dometic thermostats that run both AC & the furnace connect to a control box rather than directly to the furnace & Air Conditioner. Mine is in the air conditioner shroud. The wiring for mine has three wires at the thermostat - Ground, +12v, and control. If you have that type, I doubt any home thermostat, battery powered or not would work.
There is a replacement for the Dometic thermostat called the
Micro Air Easy Touch . It has both Bluetooth & WiFi controls as well as the faceplate. I like mine, but their website shows a replacement for your thermostat "is coming soon".