Remove the thin membrane from the back of each rack of ribs by sliding a butter utensil under it to loosen, then peeling it off with a paper towel for grip.
In a small bowl, mix together the brown sugar, smoked paprika, garlic powder, onion powder, chili powder, salt, and black pepper. Rub this seasoning blend generously over both sides of each rack.
Pour the apple juice and apple cider vinegar into the Instant Pot. Place the trivet inside. Cut each rack in half if needed to fit, then stand the ribs upright on the trivet with the meaty side facing outward, curling them around the inside of the pot.
Lock the lid, set the valve to sealing, and cook on high pressure for 25 minutes.
Once done, allow a natural pressure release for 10 minutes, then quick release the remaining pressure. Carefully remove the ribs and place them meaty-side up on a foil-lined sheet pan.
Brush a thick layer of bbq sauce over the top of the ribs. Broil on high in the oven for 3 to 5 minutes until the sauce is caramelized and slightly charred in spots. Watch closely to prevent burning.
Let the ribs rest for 5 minutes, then slice between the bones and serve with extra bbq sauce on the side.