Do you mean the 4L80-E trans? That is the one that came with the vehicle.
Regardless, the transmission shifts are controlled either by the PCM, TCM, or VCM. Now the question is this, does it slip or does it have a delayed shift? If there is a slip (no torque) when it shifts into 2nd gear, to me it sounds like it could be a pressure sensor (allowing trans pressure to drop low) or it could be an internal issue such as a worn intermediate sprag, excessive eccentricity, or the sprag is rolled over or damaged. The only way to check theses items is to remove and take the trans apart. As far as an electrical issue regarding the PCM, one of the other control modules, it should set a trans code. Also, usually the trans doesn't experience a slip, but rather failure.
I would start with checking pressure to make sure it isn't low allowing the clutch pack to slip into gear. If that checks good, I feel it may be an internal issue.
Wednesday, February 18th, 2015 AT 8:12 PM