Cook the cubed potatoes in salted water until they are fork-tender but still holding their shape. Drain and cool.

Cook the macaroni until al dente, then rinse briefly with cool water and drain thoroughly.

In a large bowl, stir together the mayonnaise, mustard, vinegar, sugar, salt, and pepper.

Add the cooled potatoes, macaroni, celery, onion, carrots, and chopped eggs to the bowl. Fold everything gently until evenly coated.

Cover the bowl and refrigerate for at least 1 to 2 hours to let the flavors meld.

Before serving, stir gently and add a little more mayonnaise if needed.