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For the pork butt: Soak 2 handfuls each of the hickory, cherry and apple wood chips in separate bowls for at least 5 hours. Pat dry and mix together. Take a large piece of foil and place the wood chip mixture on the foil. Fold the foil over to double and triple wrap the chips. Poke small holes in the foil and set aside.
Pat the pork dry. Rub with the spice mixture and set aside.
Prepare a grill or smoker with charcoal until the coals are ash white. Distribute the coals evenly and place the foil packet of woodchips on the coals. Place the pork on the grill and cook low and slow until the pork reaches an internal temperature of 190 degrees F, about 6 hours. Make sure you maintain a cooking temperature of 200 degrees F.
Remove the pork from the grill or smoker and allow it to rest for a few minutes. Once it is cool enough to touch, pull the bone out of the center. Pull the pork into bite size pieces, using two forks, and place in a large pot. Add the vinegar and hot sauce and mix well. Place on low heat until all the flavors penetrate the meat, about 10 minutes.