The most common cause of the service stability system warning has been the steering position sensor. That was without any activation of the brakes. As you are getting that symptom also, it makes the wheel speed sensors the more likely culprit. As mentioned, you'll need a shop that has a scanner capable of reading those sensors. The lateral accelerometer and yaw rate sensor also come into play, but those have been pretty reliable.

Any idea as to parts and labor costs for the WSS and other parts you mentioned?

The WSS is part and parcel to the entire wheel hub bearing assy. You can check the web for a cut-rate hub but buyer beware. I purchased a hub on the web for $89 with a lifetime guarantee. The first one lasted 1 month before it began throwing the Stability-Traction-ABS msg. on the DIC. I thought, "what are the chances of a bad new bearing?". Three months of scratching my head and $95 later for a Tech II code read from a GM dealer confirmed my suspicion. Back to the vendor I go...........

The free replacement lasted 6 mo. before it began whining/whiring/rumbling again. Under great protest from the vendor that "2 bad wheel bearings in a row is impossible" they shipped the 3rd one. I politely reminded the vendor that the 1st replacement was electrical (the internal WSS) and the 2nd replacement had a mechanical problem (the noise, but no codes). The 3rd one is holding at 1,000 miles LOL. Quiet at last and no codes. This 3rd one is the last one from that vendor, lifetime warranty or not. The DIY route is not difficult if you can turn a wrench but it is a PITA for inconvenience.

If I had to do it all over again I would order an OEM from gmpartsdirect.com. On second thought I've never had great luck with the GM bearings on Bonne'* either but at least they did not crap out in 6 mos.

As mentioned, prices, quality, and labor charges vary. This is the what the dealer would likely charge for the part and standard labor time.

Front Hub $323.46 Labor - 1.3 hours one side 2.0 hours for both
Yaw rate Sensor $349.85 No labor information listed.
Steering Position Sensor $76.22 Labor 1.3 hours
I was unable to find cost or labor information on the lateral accelerometer.