Heat gas or charcoal grill. Cut 4 (18x12-inch) sheets of heavy-duty foil; spray foil with cooking spray. Place 1/4 of potatoes and vegetables side by side on center of each sheet. Top each with 2 tablespoons dressing.
Make cuts along outside edge of each kielbasa piece at 1/2-inch intervals almost but not completely through other side. Fan kielbasa over potatoes and vegetables. Top each with 1 tablespoon remaining dressing.
Bring up 2 sides of foil so edges meet. Seal edges, making tight 1/2-inch fold; fold again, allowing space for heat circulation and expansion. Fold other sides to seal. At this point, packets can be refrigerated up to 24 hours.
Place packets, seam side up, on grill. Cover grill; cook over medium heat 20 to 30 minutes, rearranging packets several times during cooking, until potatoes and vegetables are tender.
To serve, cut large X across top of each packet; carefully fold back foil to allow steam to escape.