**if you prefer to you can boil your potatoes first then peel and dice - I peel, dice, and then cook the potatoes. Drain and lay them on a baking sheet to cool (you can speed the process up by placing the baking sheet in the refrigerator for about 20 minutes to cool the potatoes faster) Whatever method works best for you!
Cook your potatoes by whichever method above. Be sure the potatoes are cooled (or chilled) before combining with the dressing.
In a large bowl, combine mayonnaise*, vinegar, sugar, dry mustard, salt and pepper. Mix well. Taste to see if you need more of any of the dry mustard, salt and pepper.
Add celery, bell peppers, and onion to dressing and combine.
Fold in the potatoes and chopped eggs gently so as to not mash them.
*I always start with about 1 1/4 cups of mayonnaise and then after all ingredients are added, I taste-check to see if I need to add more. Sometimes I don't but there are times when I need to add a bit more.
Cover and chill.
Garnish with sliced green onion before serving.