Your original question -
Very unlikely, and I’m not sure Cornell makes a distinction between ‘grant money’ and need based financial aid; you’d still need to be found ‘in need’ to receive the financial aid. We can’t answer without knowing what the $60k in cost is for your sibling - unmet medical costs, school, training, home help? What is the age of the sibling? Even if it is $60k directly OOP and none of it is recoverable on taxes, you still have a very high family income of almost $200k, so use the NPC and see what that will provide after taking the best possible view of your situation - $250k less $60k for sibling, with a family size of 5 (6? unclear if special needs sibling is one of the two who needs to go to college after you), with one student in college. What is the NPC telling you after looking at all the assets and income in the light most favorable to you? Do your parents have other assets, like a second home or savings not in a retirement account? The NPC may say you’ll get something, but ‘something’ + $16k is unlikely to get you enough for Cornell.