In a 3-quart saucepan, cook potatoes and green beans in boiling salted water for 8 to 10 minutes or until potatoes are tender and beans are crisp-tender. Drain; set aside.
For dressing, in a blender container or food processor bowl, place mustard, garlic, vinegar, teriyaki sauce, tarragon, oil, and pepper. Cover and blend or process for 10 to 20 seconds or until thoroughly combined. Transfer to a container with a tight-fitting cover.
Toss together the cooked potato and bean mixture, tomatoes, cucumber, and onion. To tote, place in a container that has a cover. Top with egg quarters, sweet pepper strips, olives, and tuna; cover. Transport salad and dressing in an insulated cooler with ice packs. Serve within 1 hour. To serve, drizzle dressing over salad. Makes 4 servings.