1. Place the pork in a large stockpot or Dutch oven. (cut into chunks if need be to allow it to be covered with water as it cooks.) Cover the pork with water and bring to a boil over high heat. Skim off any foam as it rises to the top, during the first 15 or 20 minutes. Then lower the heat to maintain a gentle simmer and cook until the meat is tender enough to pull apart using two forks, 2 to 3 hours.
2. When the meat is done, transfer it to a large platter or cutting board, reserving the stock to use in the stew. Allow the pork to cool to room temperature. Then pull it apart and chop it roughly into small pieces.
3. While the pork is cooking, heat a large skillet over medium-high heat and add the vegetable oil, swirling to coat the pan. Crumble in the ground beef and ground turkey and cook, turning and pressing to help them cook evenly. When all the meat is cooked through, remove from heat and set aside.
4. When all the meats are ready, combine the pork, beef, and turkey in a large Dutch oven or a stockpot, along with 1 cup of the pork stock, (reserving the remaining stock to use if needed).
5. Add the whole and chopped tomatoes along with their juices, the barbecue sauce, cream-style and whole-kernel corn, Worcestershire sauce, hot sauce, pepper, and salt. Place the pot over medium heat and bring to a lively boil, stirring often.
6. When the stew is bubbling hot, lower the heat to maintain a gentle but visible simmer, and cook, stirring occasionally, for 1 hour and 15 minutes. Stir and scrape the bottom often to prevent the stew from sticking or burning; Add more pork stock, a little at a time, if the stew becomes dry or starts to stick.
7. When the stew is ready, check and adjust the seasoning. About 5 minutes before serving time, add the peas to the stew and stir gently to mix them in evenly. Cook 5 minutes more and serve hot.