Toss half the barbecue sauce with chicken and allow to rest for 5 minutes.
Preheat outdoor grill or use an indoor grill pan (if using the pan, spray with cooking spray).
Add chicken to hot grill and cook for about 5 minutes on each side; brush with reserved barbecue sauce at least twice. (Be sure it is no longer pink in the center before removing from heat).
Meanwhile, peel and slice potatoes. Boil potatoes until they are soft when pierced with a knife. Once finished, drain water. Mash with garlic powder, 1/2 teaspoon salt, butter and 2 tablespoons milk (if mixture is not to desired consistency, more milk may added 1 tablespoon at a time). Cover and set aside.
In a mixing bowl, whisk together 3 tablespoons milk, sour cream, yogurt, chopped fresh dill, vinegar, pepper and salt. Cut carrots into matchsticks and add to the dressing along with the slaw blend.
Serve chicken with potatoes, slaw and apple slices.