Anti lock light on-runs rough
I would suggest you take the vehicle to your local Auto Zone or Advance Auto Parts and have the diagnostic codes pulled. Reply back to this solution and we can go from there.
I would guess per your description, and this is only a guess until you have the codes pulled, you may have a secondary ignition system problem. If the spark plug wires, spark plugs and module / coil pack are old or original, when they get wet the ignition spark "leaks" to ground and causes the stumble or miss. The ABS light will come on because of the miss because it is disabling traction control.
Let me know what you find.
Regards,
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