If the ASD light is not on then there is nothing wrong with the ASD system. The ASD system does not work with the ABS, they are separate systems.

They share the speed sensors on the front wheels and rear diff.

The ASD system does not use the brakes to create limited slip it instead uses a set of hydraulic actuated clutches inside the diff to transfer power between the two rear wheels.

If the ASD computer, using the diff speed sensor, senses a speed differential between the rear wheels it actuates a pump which actuates the clutches.

This is just a guess but the problem you are experiencing can be caused by a worn differential. The clutches in the diff allow a torque dependent locking effect, all the time and at any speed, of up to 35% independent of the ASD. It may be that they are binding when you make a u-turn, thats usually a classic sign of a worn diff.

Redline and GM sell a Limited Slip Friction Modifier you can add to the diff to see if that will help. Also make sure the oil you are using for the diff is limited slip compatible.

Also check to see if your half shafts are in good condition.