In a small bowl, whisk together the brown sugar, paprika, garlic powder, onion powder, salt, pepper, and cumin. Rub the spice mixture over the pieces of the pork roast.
In a small bowl, whisk together the vinegar, 1 cup of barbecue sauce, and 1 cup of beef broth.
Heat the oil in the instant pot on sauté mode. Add the pork pieces to the pot, a few at a time, being careful not to crowd the pot. Cook 2-3 minutes per side, until browned, then remove to a plate. Repeat with remaining pork.
Pour the remaining 1/4 cup of beef broth into the pot and scrape up any browned bits from the bottom. Add the pork back into the pot, and pour the barbecue sauce mixture over the pork.
Put the lid on the pot, and turn the knob to seal. Cook on manual high pressure for 40 minutes. After cooking, let the pressure release naturally for ten minutes, then quick release the remaining pressure.
Pull the pork pieces out of the pot and shred with two forks, then return to the pot. Add the remaining cup of barbecue sauce and stir to combine. Serve hot.