Schools like Columbia, Chicago, Kellogg, Sloan or Tuck may be more in your range.
I just can't see HBS. Too analytical, and your leadership/team/interpersonal abilities more of an afterthought (i.e. your primary strength by far is your analytical/quant abilities, which is what has driven your career thus far). Having said that, if you really want to go, by all means apply, so long as you keep realistic expectations (treat it as a lottery ticket) and apply to a range of other schools where you have a better shot.
As for the family business, it's not really going to be a huge plus or negative - it may add some color to your application, but that's about it since it's not what you do full-time; just don't oversell it in the essays (i.e. don't try and make it a huge deal if it isn't a big part of your life in actuality; because adcoms can sense that either in the essays, and especially in the interview). And don't get a rec letter from a family member.
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