In my experience problems at low speeds (less than 10mph) when you can sometimes just feel the ABS kicking in for a split second are usually associated with bad reads from a sensor/sensors possibly caused by dirty rings or incorrect air gap between sensor and ABS ring.
Typically they occur on damp surfaces or when the wheels are not quite in the straight ahead position.
Just about every Audi I've owned over the past 30 years has suffered in this way at some point in its life. Cleaning sensors and ABS rings and making sure the sensor to ring air gap is correct usually fixes it for me.
Might not be your problem but worth a check
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