Traction control light on

Iam just saying to take it somewhere that can read traction control module codes.

Heres is the clue there is something wrong you said it shifts hard and then you cycle the key and it shifts normal. When it shifts hard its in default mode to help protect the transmission when you cycle the key it resets the code and takes it out of default mode that helps protect the transmission. Something I have seen cause hard shifts like that on those gm cars is a bad inlet air temp sensor connectors. What happens is the copper wires inside the insulation breaks causing the the transmission to shift hard in default mode.