I got my degree in anthropology and did my Senior Thesis on identifying animal bones. I'm fairly sure that's a scapula (shoulderblade), but I can't tell what kind of animal it is without a comparative collection and seeing it in person. Hope my useless degree was helpful to you
I doubt it was poisoned, people who poison dogs usually use meat, meatballs, or something a dog will gobble right up instantly. But if it was from a rotting wild animal, well, think of all the bacteria! No wonder they are vomiting.