Trim the fat cap on the top of the shoulder roast to no more than ¼ inch thickness.
In a small bowl, mix together the apple juice, water, Worcestershire sauce, salt, and sugar.
Using a metal meat skewer poke several holes half-way through the roast every inch or so into the pork shoulder. (Or use a meat injector syringe.)
Place the roast on a glass dish and pour the apple juice mixture over roast, covering and filling the holes as much as possible. Place excess apple juice mixture in fridge for later.
Brush 6-8 Tablespoons of yellow mustard over entire pork roast.
In a small bowl, combine all rub ingredients. Coat the surface of the roast evenly, pressing it into the mustard coating. Allow the roast to stand at room temperature for 30 minutes before placing it in the smoker.
Prepare the smoker for cooking between 225F to 250F. When the smoker reaches 225F, add 3 to 4 large apple wood chunks on the hot charcoals.
Using a remote wireless BBQ thermometer, insert one to monitor the temperature inside the smoker temperature and the second into the middle of the pork roast to monitor the internal temperature of the meat. Set meat internal temperature to 160F.
Smoke the pork roast fat side up over low heat, keeping the heat in the 225F to 250F range for 5 to 6 hours.
When the internal reaches 160F, remove the pork roast from smoker and place on heavy duty aluminum foil. Pour the remaining apple juice mixture over the roast and seal shut.
Return the pork roast to the smoker and insert wireless BBQ thermometer probe into center of meat (alongside the shoulder blade bone) and let cook until the internal temperature reaches 190F (3 to 5 additional hours). Remove from smoker and let rest in the foil for one hour.
Unwrap the roast and use shredding tongs to shred the meat thoroughly, discarding the bone, sinew or excess fat.