Hey Joe,,
The dual AC system in your 94 burban shares the same compressor, condenser, and Coolant (134a)..The only independent components are the evaporator (and accumulator bottle ?? I think) ,,,but the front and back passenger compartments both have their own evaporators ,, that I know for sure...
Some inherent known problems with these dual systems is when the front is being used and the same time the back is not (or fan for the back AC in OFF position) this shortens the life of the rear evaporator by half ....You should always turn the fan at least on Med or Low to the back as well when your using the front AC.. This ensures that you blow air across the rear evaporator while the system is on,, remember when coolant is traveling through the evaporator it MUST have air blowing across the fins in order to pickup heat...
In reading your note ,,,, It sounds like you may have smoked your rear evaporator..
P.S.
Do you know if your dealer replaced the line orifice filter located in the coolant line just before the condenser (right behind the passenger side marker light in the grill) this gets clogged very easily and has been known to blow out compressors...
Slyder...