You will not be able to take out any loans for which you will need your parents as consigners.
You say they are living on their savings (Dad) and odd bits of income (Mom). I cannot imagine they have any credit if there is no income to make payments with. Borrowing on their house is a huge risk in this situation and worth going to Stony Brook. If they have other assets they could easily liquidize you can discuss with them whether they could give you a loan. When will your sibling go to college?
Your budget is the 50 K that has been saved for you and the 26 K you can take out in student loans, possibly 45 K if your parents can’t take out further loans for you. That could make Georgia Tech work. I would contact them ASAP. Also all other schools that are still in the running on whether they can offer you deferred entry.
Then you go to France for a year, in order to get it out of your system and hope for one or several options to work out.
Something will come up to make Cambridge affordable (Just kidding. Sorry, it sucks, because the UK system sounds like it might work best for you, but it is not affordable, period. Not an option.)
You might love and excel in the French system. You stay on to try for Polytechnique or Normale or whatever. Whatever you do in France will be affordable at least. Might even make you happy.
You go for another round of applications for scholarships at American universities and colleges, applying strategically with the central goal of getting COA down to your budget, and enrol at the one that works best for you as long as it works better than France. You will always have Stony Brook, right? What about Alabama?
Edited to add that it is possible that people have made mistakes in the FA process which might help with doing better in the second round, or (which I think is more likely) your parents have very good equity in a very nice house. Yes, if your parents are living on assets, they may be required to melt down their assets in order to finance college for you and your sibling, and yes, it might mean downsizing. Depending on how old your sibling is, for instance, they may very soon not have to live in a place with good schools, with a large backyard and plenty of space inside and out for kids. It is a option.
Even if you do end up enrolling in Stony Brook or another financial safety after one or two years, you will always have Paris.