Fill a large pot with the potatoes and enough water to cover them by 2 inches. Bring the water to a boil, then cover and cook on medium-high for 10-15 minutes or until the potatoes are fork-tender but not mushy.
Strain the cooked potatoes and transfer them to a large bowl. Set aside in the fridge to cool for 20 minutes.
While the potatoes are cooling, in a medium-sized bowl, combine the mayonnaise, yellow mustard, Dijon mustard, relish, and salt and pepper.
When the potatoes have cooled, transfer the mayo mixture to the bowl of potatoes and stir gently to combine.
Dice the hard-boiled eggs and add them to the bowl of potato salad, tossing to combine.
Cover and let sit in the fridge for an hour before serving.