Place eggs in a small saucepan, cover with cold water by 1 inch and bring to a boil. Cover, remove from heat and stand for 12 minutes, then cool in ice water for 5 minutes, peel and chop.
Meanwhile, cover potato cubes with cold water by 1 inch in another saucepan and add cooking salt. Bring to a gentle simmer and cook for 8 to 10 minutes until tender but still holding their corners.
Drain potatoes, spread in a shallow bowl and sprinkle with vinegar. Turn gently and cool for 15 to 20 minutes until no longer warm.
Mix mayonnaise, mustard, relish, dressing salt and pepper in a large bowl. Fold in cooled potatoes, chopped eggs, celery and red onion without crushing the cubes.
Cover and refrigerate for at least 1 hour before serving cold. Keep chilled until serving and return leftovers to the refrigerator promptly.