The back has its own R134 and radiator coolant loops, all the 'blending' takes place behind the passenger side cargo area trim. The ceiling ducts over the 2nd row are ducted down the passenger side 'C' pillar and are completely separate from the front seat vent ducting.
The front blowing warm air all the time out of both driver and passenger dash vents (while the back blows cold) means both blend actuators are busted or were driven out of their movement range*, so their guts no longer move where the computer thinks they are. Sometimes that can be fixed by a reset of the Body(?) computer. You can brute force the whole thing by just disconnecting the battery for a while. But that will also reset your engine computer settings too.
If the actuators are busted, their drive gear inside physically cracked in half off the keyed shaft they're supposed to be driving, you can sometimes hear the actuator motor trying to drive the gear back and forth across its full movement range when you turn the key on. Sounds like a low winding-buzz noise.
I don't know of a single error condition that would cause both sides dash vents to blow warm at the same time, when you have the AC on (and while you are getting cold air in the back). In my understanding both actuators would have to be malfunctioning for that to happen.
Is your vent selection control working (regardless of temp), when you choose feet, dash or defrost, does the system respond / clunk and the air start coming out of the correct places?
The actuators are a whole lot less at rockauto or some careful local shopping, than at the dealer.
There's some pictures and repair notes in my GMT800 / Vortec topic
*when you get it working again, tell everyone that setting the system to the lowest cold temp (IIRC it's 60 or 62F) doesn't make it get colder any faster and repeatedly setting the lowest setting will screw up the actuators again, as the computer keeps trying to drive them to their max range of motion. Don't max the temp selection in either direction, cold or hot.