I had a problem that was similar in a 2007 Tundra. I would be riding down the rode and all of the sudden the dash would go nuts. The truck went just plain crazy, shifting would get real jerky and it would feel like the damn wheel was fixing to fall off.
The first time it happened, I pulled over, turned it off, and looked under the hood trying to figure out what the hell was going on. When I tried to crank it back up it was as if there was no battery under the hood. I called a wrecker to come tow me to the local dealership. While I waited, I disconnected the battery for about 20 minutes. It has already been mentioned but this resets the computer. When I hooked it back up it cranked and drove fine.
I drove it straight to the dealer and they could not figure out what was wrong with it. They told me to bring it back when it was doing it again. The next time it happened was months later and I was up in the delta (live in Madison). Did the exact same thing as last time and reset the computer, it drove fine.
Took it to the dealer and told them to keep the damn thing until they figured out what was wrong with it. They had some regional guy come look at it and had no ideas. I got on a toyota tundra message board and searched for a few hours until I found a problem that sounded similar to mine.
Turns out that when my truck was made, there was a problem with the plug in the number 6 cylinder being tightened down. When you hit a bump just right it would cause the plug to jump and make the computer go crazy. Once you shut off the truck it would not allow you to crank back up because the computer had shut it off trying to prevent further damage.
I drove to the dealership, met with the service manager, and they pulled my truck in to take a look. Sure enough, the number six cylinder had never been tightened down.
A month or so later I got the recall notice to have it fixed. Turns out in the San Antonio plant where my truck was made, every truck made during a 3 month span had the exact same problem.
The dealership would have never figured it out. Luckily, Toyota is pretty good now with issuing recalls if there is a known problem.
I would search real hard online and try to find the solution yourself. Even post your problem in a chevy forum and I bet you will find your answer there.
Do that a quit buying Chevy's. I know you had trouble with Toyota but the 7 in my extended family have had very very few problems compared to the two Chevy's I have owned that once you past 40,000 had nothing but problems.