2006 Silverado, with a/c running and cold on both sides for 2 hours or so then the drivers side gos hot passengers side cold at the same time.

Manual or automatic climate control ?
Have you had the HVAC control panel checked for DTC'S - diagnostic trouble codes ?

Air Temperature Sensors
The air temperature sensors are a 2-wire negative temperature co-efficient thermistor. The vehicle uses the following air temperature sensors:
• Ambient Air Temperature Sensor
• Inside Air Temperature Sensor Assembly
• Upper Left Air Temperature Sensor
• Upper Right Air Temperature Sensor
• Lower Left Air Temperature Sensor
• Lower Right Air Temperature Sensor
A signal and a low-reference circuit enables the sensor to operate. As the air temperature surrounding the sensor increases, the sensor resistance decreases. The sensor signal voltage decreases as the resistance decreases. The sensor operates within a temperature range between -40°C (-40°F) to 101°C (215°F). The sensor signal varies between 0-5 volts.
The input of the duct air temperature sensors are different from the ambient and inside sensors. The HVAC control module converts the signal to a range between 0-255 counts. As the air temperature increases the count value will decrease.

• DTC B0174 Output Air Temperature Sensor (Upper Left) Circuit Range/Performance
• DTC B0179 Output Air Temperature Sensor 2 (Lower Left) Circuit Range/Performance
• B0414 is for the left air temperature actuator.
B0408 is for the left air temperature actuator.
DTC B0989 Output Air Temperature Lower Sensors Correlation
The HVAC control module monitors the upper left and upper right duct temperature sensors when the mode switch is in the VENT or BI-LEVEL positions. The HVAC control module monitors the lower left and lower right duct temperature sensors when the mode switch is in the DEFOG, FLOOR or FRONT DEFROST positions. The duct sensors are used to measure the temperature of the air exiting the ducts to help maintain a consistent cabin air temperature. These duct sensor inputs provide the HVAC control module a way to determine if the engine needs to be started to maintain a specific air temperature. If an upper duct sensor circuit failure is detected the HVAC module will not request an engine start to help cool the cabin. A lower duct sensor circuit failure will not prevent the engine from starting.
DTC B0990 Output Air Temperature Upper Sensors Correlation
Your best bet , take it to a qualified repair shop .