Cook potatoes in boiling water until tender, about 15-20 minutes; drain thoroughly. Place in a bowl; cool slightly. Pour salad dressing over warm potatoes; toss to coat. Add celery, green pepper, onion, radishes, parsley, salt if desired and pepper; mix well. Combine the mayonnaise, mustard and sugar; pour over potato mixture and toss to coat. Cover and refrigerate for at least 2 hours.