You are correct, the Atwood is an excellent choice. The thing is designed to operate based on a different premise than most manufacturers use. But your experience is not a fault of the Atwood design, perhaps it is a faulty unit, but I suspect a more faulty installation.
PS I am not a spokesman for Atwood.
The old installation used Dometic, but how large is the coach? How is the air taken in and let out - I assume ducts. What did the ducts look like that were taken out - are you sure that the unit has the separator in place to keep the intake and output apart? Only one unit? What is it a fifth wheel?
How did he run the wire for the thermostat - through the ducts on the surface or something else? Or did he splice the old into the new? If he did, check the continuity of the wires. Since the furnace doesn't work, that could be bad and not show up as obvious.