Wow, that is a tough situation. I would imagine that is a cultural thing for her. Blood is very thick in the Indian culture and it is not unusual for multiple fan fo and it is not unusual for multiple generations to cohabitate. I totally understand your apprehension, but fear by joining with her you also join with her culture and with that comes her family. I'm wondering though if there might be a compromise. Could you instead living close proximity, maybe next-door neighbors? That way you would have family close by, but not under the same roof. Another question you must ask yourself is, how permanent is this relationship? This is a lot to take on for short-term relationship. That is something you must decide for yourself though. What are your thoughts? Does that make sense? I really do want to be a help for you.
You are probably right. I fear your relationship with her includes taking care of her parents. If you're willing to do that you can make this work. If not I'm not too sure if You have too much of a future with her. I wish I had better words to share but I fear that is where you are.
In the end, all you can do is be honest and see what happens. Just be straightforward and let The chips fall where they may. if This is meant to be it will all work out.
I glad I could be a help! I really do hope all works out for the best.