Place the potatoes in a large saucepan; cover with water. Bring to a boil. Reduce heat, and simmer 12 minutes or until tender; drain. Place potatoes in a large bowl. Add 2 tablespoons white wine vinegar, and toss gently. Cool completely.
Chop egg whites (reserve yolks for another use); set aside.
Combine remaining 2 teaspoons vinegar, mayonnaise, and next 5 ingredients (through salt) in a small bowl; stir with a whisk. Add vinegar mixture, egg whites, red onion, and remaining ingredients to potato mixture, stirring gently to coat.