Heat a grill over medium-high heat. Spray two grill baskets with non-stick spray.
Chop the pork into bite-sized pieces and place in one grill basket.
Chop the peppers and onions into bite-sized pieces and toss with the prepared Italian salad dressing. Add to the second grill basket.
Grill the pork and vegetables, stirring occasionally, until the pork is cooked through and the vegetables are soft and lightly charred, about 10 minutes.
Divide the pork and vegetables between the sandwich wraps and drizzle with the barbecue sauce.
Spoon the coleslaw over the pork and roll up the sandwich wrap. Serve immediately.