How do aircraft stall warning systems handle (or not) asymmetric-stall situations?
They don't.  The Stall Protection Computer only considers overall body AOA as measured by vanes on the left and right side of the nose.  AOA is just one bit of data, and the SPC also is measuring G loads, yaw rates, speed wise acceleration or deceleration, pitch rates, etc. and also getting inputs on flap/slat position etc to allow for all those effects.  It computes a solution for presenting the barber pole on the speed tape, and the shaker and pusher (if installed) firing points based on the body AOA and all those other factors, not local wing AOA. 

If you yaw a swept wing jet really hard with rudder, it will roll on its back, stalled or not, just from the asymmetric lift with the sweep (full aileron may or may not be enough to counteract it - you learn this the first time you do a V1 cut in training).

In any case you don't normally touch the rudder pedals on a jet except during takeoff and landing or if an engine quits.  Yawing the plane also makes the vanes show radically different angles because of the changes in airflow around the nose when skidding or slipping, and you will get some kind of mismatch related error message.

On a jet with heated leading edges, if you had ice on the wings, the SPC will be fooled and can't account for this, and the wing will stall at a lower AOA than the SPC's computed solution and the airplane may depart when the barber pole still shows good margin, and before the shaker goes off.  A nasty surprise.  Ice on one wing and not the other just means when it goes, before shaker, it will roll really hard.