Peel the potatoes and place them into one or two large pots. Cover with salted water.
Bring to a boil over high heat.
Reduce the heat to medium-low and simmer for 1 to 1½ hours, or until fork tender.
Drain the potatoes and rinse under cold water until cool enough to handle.
Cut the potatoes into bite-sized pieces.
In a very large mixing bowl or disposable foil pan, combine the chopped eggs, black olives, green olives, diced dill pickle chips, and finely chopped onion.
Add the chopped potatoes and gently mix.
In a separate bowl, whisk together the mayonnaise and yellow mustard.
Fold the dressing into the potato mixture until evenly coated. This Fourth of July Potato Salad should be creamy without becoming mushy.
Cover and refrigerate for at least 2 hours before serving for the best flavor.