I think it is probably unrealistic to expect your family to be quiet, especially as quiet doesn't seem to be a baseline for your parents. However, there are likely to be other solutions to that too, although you may have to get creative.
My family had to work with noise/homework issues too. And with having one computer with six of us in school and expected to have access to a computer. We solved both issues mostly with communication and time-of-day timing... it is usually very quiet at 4 am. Although that might not work as well for you because you will have less issues with sleepiness if you get regular sleep. Or it might if you can sleep through the noise or use white noise and ear plugs and make your "night" from 8pm to 4am or 7pm to 3am. Or 3 pm to midnight. I tended to do the 8 to 4, my daughter the 3 to midnight, so it can work. We could both sleep through what we couldn't study through.
Local library? Your church or a local church that might know you well enough to trust you to borrow a table in an empty room? Friend's house? Perhaps an elderly woman or couple who could use a friendly greeting as you come and go. Or someone who wouldn't mind having someone keep their dog company during the day. If your family has a friend who owns a business, what about the staff break room at their business?
I've done hundreds of hours of studying in a car over the years. In my case it was because I was waiting for my kids (five kids + many years + mulitple activities for each kid + no cell phones = lots of waiting) but the reason doesn't matter so much as that it can work. You wouldn't want to do all of your homework there but perhaps enough.