I have 04 z71 with 80,000 on it. When it shifts from 1st to 2nd it shakes. But its fine when shifting in the rest its fine.

 

Might be the problem lies in motor mounts, mounts will cause the jerkiness your feeling. More noticeable changing from 1st to second because there is more torque in the lower gears and the torque reaction will make the motor jump around a lot, and it would be more noticeable under heavy acceleration. Make sure about that if it has a fault, replace asap, also you might be have the problem in shift solenoids in the transmission, sometimes these solenoids will not get proper voltage for whatever reason and the pressure wont be enough to let it shift, check that too.

 

Thanks have not thought about the mounts