Begin by preparing the coleslaw salad. In a large bowl, combine the mayonnaise, sugar, buttermilk, lemon juice, white vinegar, salt and pepper. Whisk until smooth. Add the coleslaw mix (cabbage and carrots), sliced onion and sliced red bell pepper. Then toss to coat. Cover and place in fridge for at least 1 hour.
Meanwhile, prepare the sweet BBQ sauce. In a medium pot, combine the remaining ingredients (except for the shredded chicken and hamburger buns) over medium-high heat. Whisk until smooth, bring to a boil, and then reduce heat to low. Let sauce simmer, stirring occasionally for 45 minutes. Stir the shredded chicken in the BBQ sauce until heated throughout.
Toast the hamburger buns.
Place about 3/4 cup of the BBQ shredded chicken on the bottom half of a hamburger bun, followed by about a 1/2 cup of the coleslaw salad; finish with the top half of the hamburger bun.