Combine 1 cup vinaigrette and 1 tablespoon rosemary in a large resealable plastic bag. Add chicken thighs and drumsticks. Seal bag and turn to coat. Refrigerate for 1 hour.

Combine remaining rosemary, raspberry jam, 4 1/2 teaspoons vinaigrette, lime juice, soy sauce, and garlic powder in a small bowl.

Prepare an outdoor grill for indirect medium heat and lightly oil the grate.

Drain and discard the marinade. Place chicken pieces skin-side down on the grill rack. Grill, covered, over indirect heat for 20 minutes. Flip. Grill, basting occasionally with raspberry jam mixture, until a meat thermometer inserted into the center reads 180 degrees F (80 degrees C), 10 to 20 minutes more.