You went to a good school and work in financial services - you're not unconventional.
Sounds like you will apply to H/S/W no matter what others will say (which is fine - go for it), but I wouldn't limit myself to those schools. Look at Kellogg, Sloan, Booth, Columbia, Tuck, LBS and INSEAD as well. In fact, I'd pick 1-2 of H/S/W, and the 3-4 from the second list and you should feel good about applying to schools in your range.
As for your father's illness, be careful about milking it. It's unfortunately not *that* unusual. I've dealt with quite a number of clients who had to cope with a parent passing away while they were working or in school, so while it's understandable, it's not really something you can or should turn into a narrative or theme in your essays. In other words, it's essentially a data point in an optional essay - simply disclosing a fact that you took 2 years to take care of your father (basically what you explained below is about all you need, and nothing more).
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