So one press of the ESP off button while moving basically just turns off the Traction Control and allows you to spin wheels on loose traction surfaces. If you come to a full stop, put the trans in park, and with the engine running press and hold the ESP off switch for 5 seconds, you'll get a chime and a message on the EVIC saying you're in ESP Off Mode. BTW, if you have QTII or QDII, and go into 4LOW, the ESP will go off, just like if you did the long press.
In snow/gravel/sand, it may be more effective to spin wheels to get going, but you'd want to maintain stability control and not spin out. So the momentary press of the ESP off button will disable traction control and allow you to spin wheels on loose surfaces.
If you're driving slowly in deep mud/snow/sand, you don't want to loose momentum, you'll accept slip sliding latterally and fish tailing to keep your momentum and have enough experience to do it, the ESP will prevent this and could kill momentum as it applies brakes to prevent you from fish tailing or slip/sliding latterally. This is when you want to do the long press of the ESP off to turn off the ESP as well as the traction control. (If you have 4LOW, this is the situation you'd want to go to 4LOW which do the same as the long press of the ESP off button).
Of course if you're in 4LOW, you're not likely to get up to 40mph, and if you driving above 40mph in any condition, you'd be stupid to have the ESP off, so it automatically turns itself back on till you get below 35mph again.
So, from the short description you gave of the surface you're going to drive on, doesn't sound like you needed to switch ESP off, either short or long press.
BUT, even if the ESP is totally off from a short press, and one wheel is off the ground with no traction, you should not loose torque to all the other wheels.
I have had two wheels off the ground (opposite sides/opposite ends/teeter totter) in my QTI Commander and did not loose torque to the other wheels with traction.
Like mentioned the ABS pump will activate to apply brakes to spinning wheels without traction, to redirect torque to the wheels that have traction. It does this by monitoring wheels speed, and will use the brake to limit the spin of wheels to stay within a certain amount of the others. i.e. allow enough difference for the vehicle to turn but not enough difference in wheels spin to allow a wheel with no traction to spin ineffectively.
Also mention, this "Brake Traction" system is reactive, meaning its reacts to it happening and then applies the brake to fix it. So its not as effective as a true locking differential, like in QDII, but its still very effective and does work.
Turning ESP Off, either short or long press, does NOT disable this feature at all, the Wheel spin limiting feature. The only way to disable it is too disable the entire ESP system or the ABS. which you would have an ABS/BAS/ESP light on the dash.
Remember, this system doesn't magically prevent the wheels with traction from loosing grip and spinning. You can still get stuck with the system. Off Road ability is more about suspension and weight distribution than drivetrain, so that you put pressure on all 4 wheels to get traction on uneven surfaces.
So based on your short description, I can only guess one of three things happened in your case:
1.) Not knowing how the system works, perhaps you mistook the slow spinning of the air borne wheel or its reaction time, that might take a moment or two, as it not working, in reality if you kept at it, it would have worked, or perhaps you didn't have enough traction on the wheels on the ground to keep moving because of suspension limits?
2.) Your ABS or something else in the system is NOT working, and thus the Brake Traction System can NOT work.
3.) You mentioned you were in Mexico, perhaps the Mexican version of the Commander doesn't have all the equipment of the U.S. version.
If you loose traction on some wheels, the brake traction system will come into play, and since it uses the ABS system, you will hear the ABS Pump go off. When I have driven my QTI Commander up a wet, grass covered, steep incline, it went up prefectly stable and straight, but the whole time I could hear the "Chunk, Chunk, Chunk" sound and vibration of the ABS pump going off, to stop the spin of different wheels on the wet grass as they went over it, to keep torque to the wheels that did have decent traction at the time.
When I teeter tottered my Commander on two wheels on the crest of a steep small hill, it slowed down significantly, the ABS pump, Chunk, Chunk, Chunk'ed as it kinda of inched forward in surges, but it kept going till I tipped forward and got 3 wheels on the ground, and then it moved normally despite one wheel being in the air.
When I pulled to the side of a snow covered road, to have the snow collapse (since it was hiding a gully on the side of the road), I had all 4 wheels in the snow, but since my suspension was limited in how far it could travel, and my underbelly was high centered on the snow, I could not get enough pressure on all 4 wheels or even two wheels to get enough traction to overcome the snow. The ABS pump, Chunk, Chunk, Chunk'ed, the tires spun at the same speed, I couldn't get unstuck. And the the Toyota that I pulled to the side to let pass in the opposite direction had to stop and pull me out.