Sorry to hear about the personal health issues. Will keep your family in my thoughts. Now to your candidacy, I really like your profile outside of your GPA. 2.7 is really low for most schools but you are targeting the best of the best here with HBS and Stanford so red flags can really hurt your candidacy. On the positive side you are a diverse (female, minority) candidate with a fantastic GMAT score if you can score higher then the case you are making that your low GPA was the result of family/health issues has a bit more merit but this still will not totally liberate you. I would make sure all of the other elements of your profile are A+ and use any optional essays to highlight your circumstances.
I think its worth an application so take your best shot! Good Luck!
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