So my Tahoe ('96 Chevy Tahoe 5.7L Vortec) won't switch gears sometimes. I'll try to explain in a way that makes sense. This only happens when I start the car and just drive after a cooling off period. When my engine is cool and I first start it the RPM stays at about 2, it'll jump or jerk when I put it in drive or reverse and if I start to drive the car when its doing that the truck doesn't switch gears it just stays on first gear. If I start the car let it get warm then turn it off and start it again it runs fine.

I took it to a shop and after they spent over a week diagnosing it and then another to "fix it" the problem is still the same.
Is this a common Chevy problem or is there something wrong with mine?