My Tahoe runs fine when starting from cold and when at operating temperature. The problem occurs only when after running at operating temperature you shut the engine off, wait about ten minutes and re-start with the air conditioning on it will hardly run at all when you accelerate. Go about a mile or so and begins to run fine again. So in a nut shell drive the car shut off for ten minutes re-start won't hardly go and eventually runs fine again. I changed the fuel filter, EGR valve and had the injectors cleaned.
Runs rough when air is on on 1998 Chevrolet Tahoe
This sounds like your Idle Air Control motor is not compensating for the load from the A/C compressor or that your compressor is malfunctioning, it could even be icing up. When was the last time you had your A/C evacuated and re-charged? An A/C system needs a service every 2 years of so or it can ice up and seize the compressor in areas where the A/C is used a lot.