Remove skin from chicken. Place chicken in greased 4 to 5 quart slow cooker.
Combine apple butter, chicken broth, chiles and garlic in a medium bowl. Mix well; pour over chicken. Cover and cook for 5 to 6 hours on LOW or 4 to 5 hours on HIGH. Meat should be very tender. Pull apart using 2 forks and discard bone.
Heat 2 teaspoons oil in a large skillet over medium heat. Add mustard seed and onion; cook for 1 to 2 minutes. Add apples and cook 1 minute. Add coleslaw and cook 2 to 3 minutes until cabbage is still crisp but looking slightly wilted. Add vinegar and cayenne pepper and mix well.
Spoon pulled chicken on sliced bun; top with slaw.