Rinse and pat ribs dry. Remove thin membrane from back of ribs by slicing into it with a knife and then pulling. (This will make ribs more tender and allow meat to absorb smoke and rub.)
Sprinkle meat generously with Barbecue Rub. Massage rub into meat. Wrap tightly with plastic wrap, and chill 8 hours.
Prepare a hot fire by piling charcoal on 1 side of grill, leaving other side empty. (For gas grills, light only 1 side.) Place cooking grate on grill. Arrange ribs over unlit side.
Grill 2 hours, covered with grill lid, adding 5 to 7 charcoal pieces every 45 minutes to 1 hour, and keeping temperature between 225º and 250º. Add a handful of hickory chips to the charcoal every 20 to 30 minutes. Spritz ribs with apple juice from a squeeze-trigger sprayer each time you add wood chips
Reposition rib slabs occasionally, placing the one closest to the heat source in the back and adding hickory chips and coals as needed to maintain the low temperature. Grill 2 more hours. Remove ribs from grill, and place on heavy-duty aluminum foil. Spritz ribs generously with apple juice; tightly seal. Place foil-wrapped ribs back on the grill; cook 2 more hours.
Remove ribs from foil, place flat on grill, and baste generously with Vinegar Sauce. Grill 20 more minutes. Remove from grill, and let stand 10 minutes. Cut ribs into 3-rib sections, slicing between bones.