Place potatoes into a large pot and cover with salted water; bring to a boil. (You may need two pots.) Reduce heat to medium-low and simmer until fork-tender, about 1 to 1½ hours. Start checking for doneness after 1 hour. Drain and rinse the potatoes with cold running water.
Place black olives, green olives, pickle chips, onion, and hard-cooked eggs into a large heavy-duty disposable foil pan. When the potatoes are cool, chop them into small pieces and gently mix them with the olive-egg mixture.
Combine mayonnaise and yellow mustard together. Add the dressing to the salad ingredients and mix well. Chill for at least 2 hours before serving.