Cook potatoes in salted water until fork tender; let cool and cut into 1-inch chunks. Place potatoes and the vegetables in a shallow dish or container. Pour marinade over vegetables. Cover and refrigerate for 2 hours.
Preheat an outdoor grill to medium heat.
Remove vegetables from the marinade, reserving marinade. Thread vegetables onto skewers, alternating colors. Cook skewers on grill until vegetables are lightly charred all over, about 10 minutes, basting with reserved marinade and turning occasionally.
Whisk together all ingredients in a small bowl. The marinade can be prepared in advance and held covered in the refrigerator for up to 7 days.