Preheat a grill to medium high. Make the sauce: Whisk the yogurt, barbecue sauce and 1 tablespoon each lime juice and olive oil in a bowl. Reserve 1/4 cup of the sauce for the pork; set the rest aside.
Season the pork with 1/4 teaspoon each salt and pepper. Brush the grill grates with olive oil. Grill the pork, turning and brushing with the reserved 1/4 cup sauce, until marked on all sides and a thermometer inserted into the thickest part registers 145 degrees F, 20 to 25 minutes. Transfer the pork to a cutting board and let rest 10 minutes.
When the pork is about halfway done, put the corn on the grill and cook, turning, until slightly charred, about 10 minutes. Let cool slightly, then cut the kernels off the cob. Toss with the coleslaw mix, vinegar, cilantro, the remaining 2 tablespoons lime juice and 1 tablespoon olive oil, 1/2 teaspoon salt, and pepper to taste in a bowl.
Slice the pork and divide among plates. Serve with the slaw and the remaining sauce.