I highly recommend using fresh apple cider; I managed to find some in my grocer's orange juice cooler. If you prefer a more tart cider, you can use slightly less apple cider and slightly more lemon juice.
Combine all of the ingredients in a large pot or slow cooker and lightly stir. Only add 1 cup of rum at this time -- the cooking process will evaporate some of the alcohol so we'll add the other cup later.
Bring the mix to a boil. Then, reduce the heat to low, cover, and simmer for a minimum of 5 hours, stirring occasionally. 8 hours is recommended. If using a slow cooker or crock pot, 8 hours is recommended as the temperature is far lower. Halfway through your cooking time, add the other cup of rum.