Combine sugar, paprika, chili powder, cumin, garlic powder, salt, and pepper in a bowl. Set aside.
Combine ¾ cup cider vinegar, water, ketchup, and liquid smoke in the Instant Pot inner pot.
Add the pork to the sauce.
Rub the seasoning blend over the pork.
Close and lock the lid.
Turn the pressure release valve to SEALING.
Press MANUAL high pressure and adjust the time to 50 minutes.
Let the pressure release naturally for 15 minutes.
Carefully turn the pressure release valve to VENTING to release any remaining pressure.
Remove the pork.
Shred the pork, and tent with foil to keep it warm.
Skim the fat from the surface of the cooking liquid.
Press SAUTE.
Cook until the cooking liquid has reduced to about 2 cups, about 15 minutes.
Stir in remaining tablespoon cider vinegar, and season with additional salt and pepper as needed.
Either serve the sauce over the pork, or return the pork to the cooking liquid and stir to toss in sauce.
Notes
Brown sugar: You can adjust the sugar to taste. I don't recommend omitting it.
Paprika: I like the smokiness of the smoked paprika, but you can use regular paprika if you prefer.
Chili powder: The chili powder adds flavor, but there isn't enough to give it heat. Feel free to adjust the amount of chili powder if you would like some heat in the spice rub.
Kosher salt: Or ½ teaspoon of table salt.
Pork: You can use a similar cut like a pork shoulder.