In a large, wide saucepan over medium-high heat, begin reducing 2 cups of root beer for sauce to 1 ¼ cups. Meanwhile, rinse chicken wings under cold water and pat dry. Trim wing tips and discard. Cut each wing into two pieces at the main joint. Place wings in a bowl with marinade root beer and marinate in refrigerator for 30 minutes.
While reducing root beer for sauce, preheat oven to 500°F Remove wings, drain, and reserve marinade. Season wings with 2 teaspoons salt and pepper and place on a rack over a baking sheet. Place marinade in a saucepan over medium-high heat and reduce to ½ cup. Skim foam from marinade as it reduces.
While sauce and marinade finish reducing, place wings in oven and bake until they begin to turn golden, about 15 minutes. Remove and brush with marinade. Flip wings over, brush with marinade again, and continue baking until wings are golden and glazed, about 12 – 15 minutes. Discard marinade.
Meanwhile, finish the sauce by whisking mustard and hot pepper sauce into the 5 cups root beer sauce reduction. Season with 1/2 teaspoon salt or as needed. Brush wings with the sauce, return to oven and bake until golden brown, glazed, and cooked through, about 10 minutes.
Brush glazed wings once more with sauce. Serve hot wings with additional sauce on the side.