To make the smoothies, combine 2 cups of the yogurt, 2 cups ice, 1 cup of the mango and all of the honey in a blender, and blend until very smooth. Divide among four glasses and refrigerate until ready to serve. Rinse out the blender.
Preheat the grill to medium-high heat. Combine the remaining 1 cup mango, 1/4 cup water, 1/4 cup of the vinegar, the raisins, olive oil, cayenne, tomatoes and garlic in a microwave-safe bowl. Cover with a piece of plastic wrap and microwave until the tomatoes are soft, about 3 minutes. Let cool slightly and puree in a blender. Transfer to a small bowl. Set aside 2 tablespoons for the dressing, the rest will be used for tossing with the chicken.
Place the corn on the grill, cover and cook, turning as needed, until nicely charred, about 10 minutes. Remove and keep warm.
Turn the grill down to medium and brush the grates with some of the oil. Toss the chicken thighs with half of the remaining sauce and 1/2 teaspoon salt. Arrange on the grill and cook until nicely marked and the internal temperature registers 170 degrees F on an instant-read thermometer, 8 to10 minutes per side. Baste a few times with the remaining sauce while grilling.
While the chicken cooks, whisk together the remaining 2 tablespoons yogurt, the reserved 2 tablespoons sauce, the remaining 1 tablespoon vinegar, 1 tablespoon water and 1/4 teaspoon salt in a large bowl. Toss the mixed greens and carrots together. Divide the chicken, corn and salad among four dinner plates. Drizzle the greens with the reserved dressing. Serve each plate with a mango smoothie.