Cut potatoes into ½-inch slices; cut each slice into four pieces. Place in a large saucepan and cover with water. Bring to a boil. Reduce heat; cover and cook for 15-20 minutes or until tender.
Meanwhile, place beans in a small saucepan and cover with water. Bring to a boil. Reduce heat; cover and cook for 8-10 minutes or until crisp-tender. Drain potatoes and beans.
In a large bowl, combine the red pepper, corn, celery, carrot, onions, and cheese. Add potatoes and beans. In a small bowl, whisk the vinaigrette ingredients. Pour over vegetables; toss to coat. Serve at room temperature or chilled.