Rub each rack of ribs all over with 2 tablespoons of the barbecue marinade and refrigerate overnight.
Bring ribs to room temperature and sprinkle each with 1 tablespoon of the dry rub.
Light a charcoal fire in a covered grill and set it up for indirect grilling: When the temperature reaches 225 degrees, carefully push the hot coals to one side and place a drip pan filled with 1 cup of water on the opposite side. Alternatively, bring a smoker to 225 degrees. Put the ribs on the grill over the drip pan, overlapping them slightly, and cover the grill; you'll need to cook the ribs for about 4 hours total, or until the meat pulls away from the bones and is very tender. Maintain the temperature at 225 degrees by replenishing the charcoal with a fresh batch of burning coals every hour. Every hour, drain 1/2 cup of the wood chips and scatter them over the hot coals. Add water to the drip pan when half of it is evaporated. After 1 1/2 hours, spray the baby back ribs with the Cider Mop spray and rotate them on the grill; repeat spraying every 45 minutes.
Remove the drip pan and spread the coals in an even layer. Replenish with fresh coals to make a medium-hot fire. Dilute the Sweet and Sticky Barbecue Sauce with 1/2 cup water. Brush sauce over ribs and cook for 30 minutes, turning often. Repeat brushing 4 or 5 times to build a sticky glaze. Transfer the ribs to a carving board and let rest for 10 minutes. Cut between each rib and serve. (If you would like to prepare them ahead, the glazed ribs can be refrigerated overnight. Serve cold or reheat in a 325 degrees oven.)
In a blender, puree the chopped garlic, Worcestershire sauce, soy sauce, onion and water. The marinade can be refrigerated for up to 1 week.
In a small bowl, whisk together all of the ingredients. The dry rub can be refrigerated or frozen for up to 6 months.
In a large, glass measuring cup, combine the apple juice, water and vinegar. Pour into a spray bottle and refrigerate. The mop spray can be refrigerated for up to 1 week.
Heat the oil in a large saucepan. Add the garlic, onion, green pepper and a large pinch of salt and cook over moderate heat, stirring occasionally, until softened, about 10 minutes. Add the rum and simmer for 2 minutes. Add the chili powder, black pepper, allspice and cloves and cook, stirring, until fragrant, about 3 minutes. Add the brown sugar, water, ketchup, molasses, mustard, vinegar and hot sauce and simmer over moderate heat, stirring often, until thickened, about 30 minutes.
Transfer the barbecue sauce to a large food processor and puree. Season the sauce with salt. The barbecue sauce can be refrigerated for up to 2 weeks.