@Wayne and Karen,
If would complete your forum signature to include your Oliver model, year, hull number and any other modifications that make your Oliver unique, it would allow members that may be able to help, provide answers that are specific to your question about your Oliver.
@rideadeuce just provided an answer that might work for you.
My Ollie has the original Dometic AC that came with my 2017 LE2. It is 120V AC powered and the wiring could be modified to run on 12V or battery power through the inverter, which rideadeuce and Ronbrink have done as well as replacing their original AC units with Atmos air conditioner's.
And just adding to the answers to your original question, I have replaced my original thermostat with a MICRO-AIR Easytouch. I was eating lunch when I read your original post and picked up my phone and turned my air conditioner on over Bluetooth. To be clear, my AC is plugged into my house electrical system so I can’t drive away like you would like to do, so depending on your Oliver, this may require a bit of work to accomplish.
Mossey