Pat the rib racks dry with paper towels. Remove the membrane from the bone side of the ribs and then brush on both sides with the mustard and generously rub them on both sides with the dry BBQ spice rub. Season the ribs as early as you can (ideally the night before), wrapping them well to let the flavors in the rub permeate the meat.
Prepare the grill by opening the bottom vents and adjusting the lid vents to ½ open. Fill a large chimney with hardwood charcoal and burn for about 20 mins, until the coals are partially covered with a layer of white ash. Place a 13” x 9” disposable aluminum pan on one side of the base of the grill, fill with 1” of hot water and then pour the coals onto the opposite side of the grill, steeply banking them to create a single sided fire. Scatter half of the soaked wood chips over the coals, place the grill grate in place and cover for 5 mins. Remove the grill cover, scrape the grates to clean them and oil the cooking grate. Place the ribs onto the grill over the aluminum pan with the bones down. Place the cover onto the grill with the vents over the ribs. Grill temperature should be 250-275F to cook the ribs low and slow. Cook for 2 hours –after 1 hour quickly rotate the position of the ribs and thoroughly spritz the ribs with the water/vinegar mixture. Spritz the ribs every 30 minutes going forward. Monitor the grill temperature, and, if needed, add coals to the fire or light a second chimney of coals about 20 minutes before the 2 hours of cooking time is up to re-stoke the fire.
At 2 hours, carefully lift the rack with the ribs to allow you to add fresh coals if needed (over the spent ones) and remaining soaked wood chips. Rotate the ribs and spritz with water/vinegar, then replace the rack onto the grill with the ribs over the aluminum pan. Cover with the vent over the ribs and cook for 1 hour more (continue spritzing heavily about every 30 minutes). After 3 hours cooking time, cut 2 long strips of heavy-duty aluminum foil, place one rack of the ribs onto each piece of foil, brush lightly with sauce and wrap tightly, then place back onto the cool side of the grill and cook for 1 hour longer, until the rib bones are exposed and ribs reach desired doneness (tender, but not yet falling off the bone is ideal). Unwrap the ribs and brush with additional sauce and allow to cook for another 10-15 mins to set the sauce. Remove from the grill, slice ribs between the bones and serve with additional sauce.