I crashed at Nmom's for what was supposed to be ten days between term ending and my summer job several states away beginning. I was there for a total of a day and a half before my nmom told me that if I didn't "pull my weight" (ie wait on her and do all of the household chores and sleep on the mattress her cat had peed on repeatedly) then I wasn't allowed to stay. The idea was to get me to beg to stay and do all the ridiculous things she asked. She "grounded" me and gave me this ultimatum. I immediately left. Packed a small bag of essentials, walked three miles to the train station, went to NJ and stayed with friends from school.

She's going to make it feel like you don't have options. You certainly DO have options though. I don't know where you live, but you may be able to find a room (just a room, even) for rent cheaply if you check craigslist. If you have friends you can stay with, you could even bounce between couches. My entire life fit in a backpack at your age (because if situations like this), so it was always easy to pick up and move on. Absolutely do not give her any money. You owing her is faulty nlogic. You owe her nothing. Paying a reasonable amount in rent might be justifyable, but not usually until after college. Where does she expect you to go in between?

In future, find a summer job that keeps you away. Your university likely has summer staff positions (I worked for the key depot one summer, they house you as part of your pay), or find a summer camp or summer internship that will either provide housing or hook you up with affordable housing shared with other interns.

Oh, and Change the security questions on your bank account to things your mother wouldn't know.