Put pork pieces into a large saucepan with a lid. Add cold water to cover, and then add vinegar and 2 or 3 generous pinches of salt. Bring the water to a boil over high heat, when boiling, reduce heat to simmer and cook, covered, for about 2 hours, or until pork is very tender.
Remove pork from the water and set aside to cool. Do not discard cooking water.
While pork cools, soak the ancho and chipotle chiles together in the cooking water for about 20 minutes or until soft. Reserve 1 cup of the water and discard the rest. Cut off the chile stems, then cut open chiles and scrape out and discard seeds and membranes. (Wear rubber gloves or wash your hands thoroughly with soap and hot water after handling chiles.)
Put chiles, reserved cooking water, oregano, cumin, onion, and garlic into a blender and purée.
When pork is cool enough to handle, shred it with your fingers or 2 forks.
Heat the bacon fat or lard in a large skillet over medium-high heat, then fry the pork, in batches if necessary, until crisp and brown.
Drain pork on paper towels, discard cooking fat, and wipe out skillet. Return pork to skillet, mix in sauce, and heat through over medium heat for 2-3 minutes, stirring frequently.