Combine 1/2 cup barbecue sauce, 2 tablespoons vinegar, water, and garlic in a large zip-top plastic bag. Add pork; seal bag, and marinate in refrigerator 8 hours, turning bag occasionally.
Preheat oven to 400°.
Remove pork from bag; discard marinade. Heat a large ovenproof skillet coated with cooking spray over medium-high heat. Add pork; cook 2 to 3 minutes, browning on all sides. Remove from heat, and place pan in oven. Bake at 400° for 13 minutes or until a thermometer registers 145°. Brush tenderloin with remaining 2 tablespoons barbecue sauce; bake an additional 5 minutes or until thermometer registers 155°. Remove from oven; let stand 15 minutes. Cut in half crosswise. Slice each half lengthwise into 1/4-inch-thick slices.
Meanwhile, combine remaining 1 tablespoon vinegar, mayonnaise, and next 3 ingredients in a medium bowl. Add coleslaw, carrot, and parsley; toss well to coat. Set aside.
Divide pork evenly among tortillas. Top each with 1/2 cup slaw mixture; roll up tortillas. Serve immediately.