Any car buffs out there that might know what went on with my tire today?

So it’s been a long day today. Came home from work and noticed my car’s front right tire was slowly losing air. So I packed up the kids and got on the road to go get a new tire, well I could feel my car pulling to the right and then all of a sudden the car started to shake and then the rubber of the tire completely peeled off. I pulled over and got the spare and put it on and drove the rest of the way to the tire shop.
So I got a new tire (used one) and started to drive back home, everything was fine for the first five minutes, all of a sudden I could feel the car really starting to pull again to the right and then BAM again the tire peeled off, it just peeled off the entire middle part of the tire and the walls stayed on the rim. Did I just get unlucky with a used tire, because when I put the spare on it does not pull. I don’t understand why it would do it to both of the tires. Could it be the rim itself that’s causing the tires to peel off? Just the middle part of the tires? I am not a car person, I just drive them so I have no idea.