Position a rack in the upper third of the oven; preheat to 425 degrees F. Season the chicken with salt and pepper and place on a foil-lined rimmed baking sheet. Roast until the skin is golden and crisp, about 30 minutes.
Meanwhile, make the barbecue sauce: Combine the cider, ketchup, Worcestershire sauce and 1 tablespoon mustard in a small saucepan. Bring to a simmer over medium heat and cook, stirring, until slightly thickened, about 15 minutes.
Melt the butter in a large skillet over medium heat. Add the scallion whites, bell pepper, 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring, until the vegetables soften slightly, about 5 minutes. Add 1/4 cup water, the corn, lima beans and the remaining 1 teaspoon mustard. Bring to a simmer and continue cooking until the vegetables are tender, about 10 minutes. Stir in the scallion greens.
Turn on the broiler. Brush the chicken with the prepared barbecue sauce and broil until the sauce is thick and bubbling, about 3 minutes. Serve with the succotash.