How do i remove the passenger side air vents on 03 chevy suburban

SOURCE: 2004 chevy subarban blows cold air on one side hot air on other side

i was a GM mechanic for many years, the problem you are having is one of your mode door actuators has gone bad, most of the time it is the actuator on the drivers side that causes the problems, i have seen this many times, sometimes you can take it to the dealer and they can hook the computer up to it and recalibrate it but most times it has to be replaced , it is located under the dash in the area above your gas pedal.

SOURCE: 2005 chevy 2500hd duramax driver side vents blow hot air

It sounds like the HVAC head needs to be recalibrated, most likely when you unhooked the battteries you lost the memory to the control head, it's in a default position/state.

SOURCE: 2004 chevrolet suburban AC blows hot/cold at same time

You need to replace the drivers side temp actuator that is located on the left side of the HVAC box. It is retained by 3 screws and is fairly easy to replace.

SOURCE: 2005 Chevy Impala driver's side heat blows cold.

First....buy a drivers side air flow actuator at a auto parts place for dual zone heating/cooling.
(NAPA etc will have it.....or the dealer)
Open the glove compartment.....all the way....you may have to take the screws out at the bottom......look in at the heater assembly....look over to the left....you will see the two air flow actuators.
Look at the part you have and match it to the part on the heater assembly.
The actuator that is closest to the engine is the drivers side control.
Replace it.
Try your controls and check for heat and cooling on both sides.
The stepper motor in these actuators goes bad on quite a few...but over look that.....you have a great car,good for many miles of trouble free driving.

SOURCE: the drivers side AC vents

More than likely the problem is with one of the blend doors or its actuator motor inside the HVAC unit in the dash. The repair involves a partial disassembly of the dash to access the parts. This definitely not a thermostat issue.