Obviously, your mom is under a helluva lot of stress over your Nan so cut her as much slack as you can. Part of the whole transition into adulthood is understanding your parents are only human too with their own set of seemingly insoluble problems. Keep thinking about your options and do the research before making a judgment and then follow through by taking responsibility for the outcome. Life is like a card game, sometimes we get a shitty hand to play and have to hope for a better one to in the next deal....
Having said that, it sounds like you are good student with a good head on your shoulders, so I have confidence you will muddle through somehow!