1999 Chevrolet Tahoe Shake

I have a 1999 Chevy Tahoe LT 4dr, about 170,000 miles. I know it is a V8, but do not know the engine liter size. I purchased it used about 3 years ago and this is the first problem I have had with it. It has an awful shake. It only shakes when in park and idling at a stop sign or red light. The shake is pretty bad. It causes the middle console, (between the driver and passenger seats) to shake, the whole dash, steering wheel, etc. When I am driving, accelerating or just staying at a steady speed, it runs perfect. I have taken it to one auto repair shop and the guys there had no idea what it was. They checked the motor mounts and said they connected it to the diagnostic machine and didn't receive any codes. Do you have any idea what it might be? I am a single woman and just don't want to get ripped off. If I knew more about possibilities of what it "might" be, maybe I would have a better chance.