Place pork in 3 1/2- to 4-quart slow cooker; pour one bottle barbecue sauce over top. Cover; cook on Low heat setting 9 to 10 hours.
Thirty minutes before pork is done, in large bowl, toss cabbage and carrots until mixed. In small bowl, mix remaining ingredients except tortillas with whisk until sugar is dissolved. Pour over cabbage mixture; toss until coated.
Transfer pork roast to bowl. Shred pork, using 2 forks. Skim fat off surface barbecue sauce liquid in slow cooker; pour over shredded pork. Stir in more barbecue sauce, if desired.
Using slotted spoon, spoon about 1/3 cup pork mixture over tortillas. Top with about with about 1/3 cup coleslaw; roll up.