Allow the ham to stand at room temperature for 30 minutes before grilling.
Prepare the grill for direct and indirect cooking over medium-low heat (about 350°F).
Score the ham in a large crisscross pattern about 1 inch apart and ½ inch deep on all sides, except the cut side. Place the ham, cut side down, in a large disposable foil pan and pour in the apple juice. Loosely cover the ham only with aluminum foil. Brush the cooking grates clean. Grill the ham over indirect medium-low heat, with the lid closed, until an instant-read thermometer inserted in the thickest part of the ham (not touching the bone) registers 120°F, 2 to 2-½ hours. Meanwhile, prepare the sweet potatoes.
Bring a large saucepan of lightly salted water to a boil over high heat. Add the sweet potatoes and cook until a small, sharp knife inserted into the center of the potatoes meets with just a little resistance, 8 to 10 minutes. Drain and rinse under cold running water. Let cool completely, at least 1 hour.
In a small saucepan over medium-low heat, combine the glaze ingredients and heat until the jelly is melted, whisking occasionally. Set aside.
When the internal temperature of the ham reaches 120°F, remove the foil. Brush the ham with half of the glaze and continue cooking for 15 minutes. Then brush with the remaining glaze and cook until the glaze is set and an instant-read thermometer inserted in the thickest part of the ham (not touching the bone) registers 130°F, about 15 minutes more. Remove the ham from the grill and take the ham out of the pan. Reserve the cooking liquid in the pan. Cover the ham loosely with foil to keep warm.
Brush the sweet potato wedges with the oil and season evenly with the salt and pepper. Grill the sweet potatoes over direct medium-low heat, with the lid closed as much as possible, until they are nicely marked and just tender when pierced with the tip of a small, sharp knife, 10 to 15 minutes, turning occasionally. When fully cooked, add the sweet potatoes to the pan with the reserved cooking liquid.
Cut the ham into slices and spoon as much of the remaining cooking liquid as you like over the slices. Serve warm with the sweet potatoes.
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