2002 Chevy Tahoe Shuddering noise between 1st and 2nd gear

There is a tech bulliten on harsh 1-2 shift, usually the service engin soon light is on? Here's the bulliten's first page, use the TSB# and call Chevy about it.
Information on 4L60-E M30 Rear Wheel Drive Automatic Transmission Valve Body Reconditioning, DTC P0741, P0756, P0894, Harsh 1-2 Shift TECHNICAL SERVICE BULLETIN Reference Number(s): 07-07-30-024,  Date of Issue:  September 27, 2007 Related Ref Number(s): 07-07-30-024 ARTICLE BEGINNING SERVICE INFORMATION The following new service information outlined in this bulletin will aid technicians in providing easy to follow valve body reconditioning instructions and new illustrations to simplify reassembly of the valve body. This service bulletin will also provide additional service information documents that are related to the 4L60-E transmission. Related Service Documents à   DTC P0741 - Torque Converter Clutch (TCC) System - Stuck Off. Refer to Service Bulletin 04-07-30-041. à   DTC P0756 - 2-3 Shift Solenoid Valve Performance - No First or Second Gear. Refer to Service Bulletin 01-07-30-036H. à   DTC P0894 - Transmission Component Slipping. Refer to Service Bulletin 06-07-30-007. à   Harsh 1-2 Shift. Refer to Bulletin PIP3170E. Inspection Procedure 1. Using the exploded views in this bulletin, inspect each bore for freedom of valve(s) movement and evidence of debris. Pay particular attention to those valves related to the customer's concern. 2. Verify movement of the valves in their normal installed position. Valves may become restricted during removal or installation. This is normal due to small tolerances between the valves and bores. Affected Model (s): 2004-2007 Buick Rainier; 2002-2005 Cadillac Escalade; 1997-2002 Chevrolet Camaro; 1997-2003 Chevrolet Corvette, S-10; 1997-2005 Chevrolet Astro; 1997-2005 Chevrolet Blazer; 1997-2007 Chevrolet Express, Silverado Classic, Silverado, Suburban, Tahoe; 2002-2007 Chevrolet Avalanche, TrailBlazer, TrailBlazer EXT; 2004-2007 Chevrolet Colorado; 2004 Chevrolet SSR; 1997-2003 GMC Jimmy, Sonoma; 1997-2005 GMC Safari; 1997-2007 GMC Savana, Sierra Classic, Sierra, Yukon; 2001-2007 GMC Envoy, Envoy XL, Envoy XUV, Envoy Denali, Envoy XL Denali, Yukon XL, Yukon Denali, Yukon XL Denali; 2004-2007 GMC Canyon; 1997-2004 Oldsmobile Bravada; 1997-2002 Pontiac Firebird; 2004 Pontiac GTO; 2006-2007 HUMMER H3; 2005-2007 Saab 9-7X; with Hydra-Matic  4L60-E Automatic Transmission (RPO M30) IMPORTANT: If valve body cleaning is not required, Do Not disassemble the bores unless it is necessary to verify movement of valves. Page 1 of 9 Information on 4L60-E M30 Rear Wheel Drive Automatic Transmission Valve Body Rec.

This is the fix for your concern, may or may not set a code, the valvebody needs to be removed and inspected/cleaned, can be done without removing the tranny. Not sure of the cost, but it isnt a complete rebuild.