Can't turn off the headlamps

Question edited for clarity.
Question moved to model category.

Here are all your fuses

GMC Envoy (2002-2009) fuses and relays

https://fuse-box.info > gmc > gmc-envoy-2002-2009-f...

Here you will find fuse box diagrams of GMC Envoy 2002, 2003, 2004, 2005, 2006, 2007, 2008 and 2009, get information about the location of the fuse panels ...

You very well could have a couple of faulty relays 45 & 46 in the underhood fuse / relay box . Could also have DTC'S - diagnostic trouble code's stored in the BCM - body control module .
DTC B2575 Headlamp Control Circuit
When the body control module (BCM) senses a request for headlamp or daytime running lamp (DRL) illumination, the BCM sends a pulse width modulated (PWM) ground signal to the low beam headlamp driver module through the low beam headlamp driver module control circuit. The low beam headlamp driver module will illuminate the headlamps, adjusting the intensity based on the PWM signal received.
DTC B2585 Park Lamp Control Circuit
When the body control module (BCM) receives a ground signal from the headlamp switch commanding to illuminate the park lamps, the BCM will energize the park lamp relay by grounding the park lamp relay control circuit.
DTC B3802 Park Lamps Request Circuit
The body control module (BCM) monitors the park lamp switch signal circuit and the headlamp switch headlamps on signal circuit in order to determine when the park lamps and headlamps should be illuminated. When the headlamp switch is turned to PARK, the BCM senses that the park lamp switch signal circuit is grounded and the headlamps switch headlamps on signal circuit is open. The BCM will then energize the park lamp relay illuminating the park lamps. When the headlamp switch is turned to HEAD, the BCM senses that the park lamp switch signal circuit and the headlamp switch headlamps on signal circuit are grounded. The BCM will then energize the park lamp relay and headlamp driver module (HDM) illuminating the park lamps and headlamps.
relay # 46 is the HDM headlamp driver module .

CHECK INSIDE YOUR FUSE BOX (USUALLY LOCATED UNDER THE HOOD). LOOK FOR THE RELAYS THAT CONTROL THE HEADLAMPS. TRY TO CHANGE PLACES WITH THE ONE'S THAT THE NUMBER MATCHES. GENERAL MOTORS SEEMS TO HAVE A PROBLEM WITH THESE. THE LOCATOR PICTURE WILL BE INSIDE THE LID COVERING THE FUSE PANEL BOX.

Did the car drive fine in 2wd? Sounds like you have a different problem with the transfercase. You can run bigger tires as long as they don't rub on the ball joints which may require grinding to make work. Trailblazer/ Envoy owners have put up to 35" tires on there with the same transfer case. Of course with suspension modification, but with the same transfercase and hubs.

hi ,ive got exactly the same problem on my cherokee,ther is a sound of a relay buzzzing under the dash.when i turn on the side lights,nothing,turn on headlamps and i get dip plus side lamps,no dash lights though,after a whils all lights fail but i can pull/flash main beam and hold it on,im taking out the dash area tomorrow,friday ,i have aspare headlamp switch and relay/fuse box ,my mobile is 07712128561,ill keep you posted

The headlight assembly doesn't come apart (not easily anyway). To remove it from the car, there are two L shaped tabs located at the top of the assembly, pull these straight up. This will release the assembly.

1 Gal(imp) = 1.2 Gal (US)
therefore...
21 mpg (US) = 25.2 mpg (CDN)

it could be a fuse.

This sounds like a loose connection/bad wire somewhere for the low beam lights. Can't really give you more information without seeing the vehicle, and wiring diagram for the circuit. Usually, things that go on and off when hitting bumps are connection/wiring problems. The fact that one of your low beam headlamps burnt supports this theory. Bad connections or wiring mean lower voltage, thus higher amperage at the bulb, motor or whatever it's running, which makes them burn a lot quicker.

I had the same problem on my 2005 Envoy. Turned out to be the idler pulley bearing. It is just a pulley the belt rides on. The bearing in the pulley was what was making the high pitched whine. I replaced the bearing, and the noise went away.