You should definitely send an explanatory letter to colleges at the time that you apply for aid–or as soon thereafter as possible. Do not wait until you receive your aid award. If you have documentation that backs up your explanation (e.g., the nursing home bills you pay for Grandma), send copies with your letter.
However, like most things in the admissions world, the responses to your situation may be inconsistent. One college might take your extenuating circumstances into account; the next school might not.
So, once your child has received all aid awards, you should contact the financial aid offices that were not responsive to your needs and try to appeal … unless, of course, these are not colleges that your child wants to attend.
If a college–let’s call it “College A”– does not seem to consider your special needs but another school (“College B”) does, you may be able to leverage one aid award against the other, if you prefer A over B. However, this rarely works unless the admission standards at both schools are comparable, and–even then–you have to keep in mind that even similar schools can have dissimilar financial aid policies … or budgets. Even so, it can’t hurt to try.