Cook the chicken and pork shoulder in a large pot with enough water to cover. Bring to a boil, then reduce heat and simmer until meat is tender, about 1 hour.
Remove meat from pot, let cool, then shred.
In the same pot, add the shredded meat, crushed tomatoes, diced tomatoes, creamed corn, whole kernel corn, chopped onion, barbecue sauce, Worcestershire sauce, apple cider vinegar, brown sugar, salt, black pepper, cayenne pepper, and chicken broth.
Bring to a boil, then reduce heat and simmer for 1 hour, stirring occasionally.
Notes:
This stew is perfect for a cold day and can be made ahead of time for easy meals.