How to Make It
Place the pork in a 5- to 6-quart slow cooker. Rub with the brown sugar, chili powder, garlic, 1 teaspoon salt, and ¼ teaspoon pepper. Add ½ cup of the vinegar and ½ cup water.
Cook, covered, until the meat is tender and shreds easily, on high for 4 to 5 hours or on low for 7 to 8 hours (the low setting will make total cooking time 8 hours, 10 minutes).
Meanwhile, in a medium bowl, whisk together the mayonnaise, sour cream, granulated sugar, the remaining 2 tablespoons of vinegar, and ¼ teaspoon each salt and pepper. Add the coleslaw mix and toss to combine; cover and refrigerate until ready to serve.
Before serving, transfer the pork to a bowl, discarding the liquid. Using 2 forks, shred the meat. Mix in the barbecue sauce. Serve the pork on the rolls with the coleslaw and the pickles and chips, if desired.