Place the ham in a large pot and cover with 2 parts water to 1 part vinegar until the ham is covered by at least an inch or two of liquid. Bring to a slow boil and cook for approximately 3 hours (without a lid) or until the meat falls off the bone. Depending on the size of your ham, you may need to adjust the length of time you boil your ham. You should not be able to remove the ham without it falling apart.
Carefully remove the ham and cool for 30 minutes or until you can touch the ham without burning your fingers. Shred the ham or cut into large chunks and place in a large container and refrigerate. I save a cup or two of the ham broth to use to make gravy. Otherwise discard the broth and bones.
Place ham in a 9×13 baking dish (You may not need all your ham). In a small bowl, combine Coca-Cola, brown sugar, balsamic vinegar and ground mustard together. Pour over ham. Cover with foil and bake at 325 degrees for 1 hour.
You can also reheat the ham in a crockpot, which is what we did during the holidays. Our oven was already full, so this was just easier. We put the ham and brown sugar coke mixture in the crockpot on low about 3 hours before serving.