We don't have the info needed on which floorplan of that year and model of RV, so we are limited in looking up much info as it is filed year model and floorplan.
With nine different RV in that group, our odds of hitting the correct one are pretty slim!
But much of the problem may also be more a chassis question than RV as the RV is built on a stripped chassis. So much of this area can be somewhat on the border whether you need chassis info or RV info, depending on who added which exact parts.
Can you spot which RV you have as that can let us take a look at how it might be built and sometimes make better suggestions?
One item that is semi easy to check and can be verified by a close look, is how the controls may be working.
The dash controls are often airline from that control head to other places where various valves and flaps open and close for the different heat/cool/defrost changes.
One thing to check is what happens when the controls are changed from heat to cool, etc. Various types use different controls so this is just a possible thing to check but it is somewhat common for the rubber tubing that uses engine vacuum to move things gets brittle and leaks!
One thing that can happen is when the valve that cuts off hot water flowing though the heater stops closing. It often is easy to spot as it set in a hose between the engine and the heater and has a vac line on it. If the valve to cut off hot water doesn't close, it may simply overwhelm the AC trying to cool the air! The AC may be cooling but you can't tell it because there is so much hot air going inside!
One low cost/low tech idea is to find that valve and see if it moves when the controls are changed from heat to cool!
It might be worth the time to take a look under the hood and verify this type vale is moving?
Almost certainly not the one you have as there are hundreds but this might be a general idea to look at something simple like leaking vacuum lines?
Good luck on the chase. I like to check the cheap, easy fixes first before diving into the tough stuff that I can't see!