Add water and chopped potatoes into the bottom of the Instant Pot insert. Place uncooked eggs in their shell on top of the potatoes.
Secure the lid and turn the valve to sealing. Select high pressure and set the time for 4 minutes.
When done, quick release the pressure and immediately remove the eggs to a bowl of ice water to stop the cooking. Drain water from the potatoes.
While the potatoes and eggs are cooking, whisk together the mayonnaise, milk, lemon or pickle juice, and sugar in a small bowl. Taste and season with salt and pepper.
Pour the dressing over the warm potatoes. Chop the eggs and add them to the bowl. Stir gently, cover, and refrigerate for a few hours to let the flavors blend and the salad to chill.