Preheat the oven to 350 degrees. Trim the excess fat and use the tip of your knife to make 1/4-inch deep scores all over the surface of the ham in a diamond pattern. Place the ham in a large (preferably nonstick) roasting pan and pour 1 ½ cups of the ginger ale and ½ cup of the rum over the meat. Tent loosely with foil and roast 1 hour and 15 minutes.
While the ham roasts, combine the remaining 3 cups ginger ale, remaining ½ cup rum, brown sugar, apple jelly and Dijon in a saucepan; stir until well-combined and bring to a boil. Continue to boil gently until it is thickened to a syrupy consistency, 45-50 minutes.
After the ham has cooked for the initial 1 hour and 15 minutes, remove the foil. Brush the ham with some of the glaze. Return it to the oven and roast for 15 minutes, and again brush with glaze. Continue roasting and brushing every 15 minutes until a meat thermometer inserted in the center registers 145F degrees, about another 1 hour and 15 minutes.
399 calories, 26 g protein, 13 g carbohydrates, 0 fiber, 25 g fat, 8 g saturated fat, 1414 mg sodium