If your butcher has not already done so, remove the thin silverskin membrane from the bone side of the ribs by working the tip of a butter knife or screwdriver underneath the membrane over a middle bone. Use paper towels to get a firm grip, then tear the membrane off.
In a small bowl, combine mustard, 1/4 cup apple juice and Worcestershire sauce. Spread thinly on both sides of ribs; season with rub.
Prepare your smoker or grill for indirect cooking and bring temperature to 235 to 240 degrees with wood chunks or wood chips and charcoal. Smoke ribs, meat side up, for 3 hours. Transfer to a rimmed baking sheet, but leave smoker hot.
Tear off 4 long sheets of heavy-duty aluminum foil. Place 1 rack of ribs on each of 2 pieces of foil and pull up sides to keep liquid enclosed. Sprinkle half the brown sugar on 1 rack, then top with half the honey and half the remaining apple juice. (Use a bit more apple juice if you want more tender ribs.) Lay another piece of foil on top and tightly crimp edges to prevent leakage. Repeat with remaining rack. Return foil-wrapped ribs to smoker and cook an additional hour.
Carefully remove foil from ribs (watch for hot steam) and brush ribs on both sides with barbecue sauce. Discard foil. Arrange ribs directly on grill grate and continue to smoke until sauce "tightens," 30 minutes to 1 hour more or until meat has shrunk back from bones a few inches. Let ribs rest for a few minutes before serving.