Preheat your smoker to 250°F. Trim any excess fat from the surface of the pork shoulder.
Prepare the dry rub by combining brown sugar, paprika, salt, black pepper, chili powder, and red pepper flakes in a small bowl.
Apply a thin coating of yellow mustard to the entire pork shoulder and cover evenly with the dry rub.
Place the pork shoulder on a mid-level rack in your smoker and let it cook for five hours.
Combine a small amount of equal parts apple juice and apple cider vinegar in a spray bottle.
Remove the pork shoulder from the smoker and spray it with the apple juice mixture before wrapping it tightly in aluminum foil. Once wrapped place it back into the smoker to cook for another two to three hours.
During the final hours of cooking, prepare a sweet barbecue sauce by combining ketchup, brown sugar, apple cider vinegar, dijon mustard, salt, black pepper, chili powder, and water in a medium saucepan.
Heat the mixture over low heat for around 10 minutes, stirring constantly.
Once the internal temperature of your pork shoulder reaches 190°F, remove from the smoker and let it rest for 30 minutes.
Shred the pork with forks, tongs, or gloved hands and enjoy!