Sounds like you have a very competitive application already. I don't know you specifically, of course, and I could be completely off base here, but you did a lot of really impressive things in your undergrad time. Good job. But, how would you assess your ability to socialize/have a conversation with a new person/have fun? I think these traits make an interviewee much more personable and interesting. A gap year to sort of relax/decompress/pursue other NON-MEDICAL interests would be a good idea so that way when it comes time to work on your application and MCAT, you aren't so burnt out.
Taking care of your family is a very impressive leadership quality, don't negate that. It shows a high level of maturity on your part.