Wash, peel, and cut the potatoes into about ¾-inch cubes.
Place the cubed potatoes in a large pot and cover them with water. Add salt to the water.
Bring the pot to a boil, then reduce the heat to simmer. Cook the potatoes until they are tender but still firm, about 10-15 minutes.
Take care not to overcook them so they hold their shape.
Drain the cooked potatoes in a colander and immediately sprinkle them with white vinegar.
In a small bowl, whisk together the yellow mustard, mayonnaise, and pickle relish.
In a large mixing bowl, combine the warm potatoes, finely chopped hard-boiled eggs, minced sweet onion, and prepared dressing.
Gently toss everything together to coat the potatoes evenly.
Add salt and pepper to taste. Adjust seasoning as needed for the best flavor.
Serve it warm or refrigerate for several hours to let the flavors meld.