Place the quartered potatoes in a large pot and cover them with cold, salted water. Bring to a boil and cook for 15-20 minutes, or until fork-tender but not mushy. Drain immediately and let cool slightly.

While potatoes are cooking, prepare the hard-boiled eggs. Peel and coarsely chop them once cool enough to handle. Set aside.

In a large mixing bowl, whisk together all the dressing ingredients: mayonnaise, yellow mustard, sweet pickle relish, apple cider vinegar, sugar, salt, and pepper until completely smooth and well combined.

Gently fold the warm potatoes into the dressing. The warmth helps the potatoes absorb the flavor. Add the chopped celery, red onion, chopped eggs, fresh dill, and celery seed. Mix very gently to avoid breaking up the potatoes entirely.

Taste the salad and adjust seasonings (more salt, pepper, or vinegar if needed for tanginess). Cover the bowl tightly with plastic wrap.

Refrigerate the potato salad for a minimum of 4 hours, or preferably overnight, to allow the flavors to fully meld and develop. Serve chilled.