Rachel, keep in mind that your mother and sister are simply
projecting their own fears onto your situation. When they ask things like "Why would
you want to carry a gun?", what they are really saying is "
I am scared of guns and would never carry one". Their reasons for not liking guns are fear- and emotion-based-- not logical. Tossing facts and figures might help a bit, but a total turnaround probably won't happen until they conquer their fear. And keep in mind that their fear might not necessarily be fear of guns, but perhaps fear of self-reliance or fear of conflict. Your choosing to carry a gun might be bringing up some ugly truths they don't want to face-- truths like "we're vulnerable" or "there are predators out there". Many people take the "ignorance is bliss" attitude and are content to stick their heads in the sand.
For a quick read, that hits on facts AND emotions, I recommend
40 Reasons for Gun Control
Good luck!