Preheat the smoker to 225 degrees Fahrenheit.
Place the ham meat-side down in a large disposable roasting pan. Using a knife, cut score marks across the entire surface of the ham about 1 inch apart and 1/2 inch deep in a diamond pattern. Drizzle the ham with the yellow mustard, using your hands to spread it across evenly. Generously season the outside of the ham with the sweet and smoky rub.
Transfer the pan with the ham onto the smoker grates. Close the lid and smoke the ham for about 6-7 hours, or until the internal temperature of the ham reads 165 degrees Fahrenheit.
In a medium saucepan, combine all the sauce ingredients. Over medium high heat bring the sauce to a boil, stirring constantly. Once sauce comes to a boil lower heat to medium and simmer for 15 minutes, stirring constantly.
Once your ham reaches 165 degrees Fahrenheit, carefully take the ham off the smoker and increase the heat to 300 degrees Fahrenheit.
Pour apple juice into the bottom of the pan with the ham in it and then pour the glaze over the top of the ham. Cover the pan tightly with foil.1 cup apple juice
Once the smoker is preheated to 300 degrees Fahrenheit, place the covered ham onto the smoker, close the lid, and continue cooking the ham until the internal temperature reads at least 200 degrees Fahrenheit and your thermometer probe slides into the meat like it is sliding into softened butter. This should take bout 2-3 hours.
Remove the ham and let it rest for at least 30 minutes before shredding. Pour any remaining juices from the braising pan over the shredded ham before serving.