When ABS or traction control kicks in-out on a Regal GS you'll feel it in the steering because with the full range traction control system it will apply the brake. The lights indicate its probably one of the wheel sensors. To determine which specific wheel sensor is causing the problem, it has to be scanned with a scanner capable of detecting GM CHASSIS/ABS codes otherwise it is just a guess.
Replacing the hub/bearings is very tedious but can be done DIY. You'll need special tools like a torque wrench, breaker bar, 35 - 36mm socket for the axle nut. If the hub is stuck on the spindle you'll need a hub puller. When the job is completed the axle nut must be torqued to a range of 151 - 180 ft lbs depending on whether you use OEM GM parts or aftermarket.
2001 Buick Regal GS