You need to upgrade the transfer case fluid to AutoTrac II (blue fluid only sold at GM dealers), change the tranny fluid to DEXTRON VI. That will fix the shudder and shake issue- that issues is AWD related and occurs and very low speeds, typically when turning. It is also a good time to change your front differential fluid (very easy).
The traction control can be many things, from sensors on the wheel bearings as a starting point. I would first update the drive train fluids as mentioned above and then see how the traction control system is working. Failure to update the fluids on your AWD SUV typically results in premature transmission failure. Updated the fluids makes your AWD system run great.
2001 Bonneville SSEi, 219,000 miles.
Whats in my driveway:
1998 Chevy S10 4x4 ZR2, 1999 Olds Bravada, 2001 Pontiac Bonneville SSEi, 2007 Ford F-350 regular cab 2WD, 2008 BMW 335i coupe (Wife'* replacement for her Bonneville). The Bonneville is my favorite of all the cars in the driveway.