welcome here! 
the best way to convince your parents is by example. if they can see your rabbit does not cause any problems, they *may* be more lenient as to where she’s allowed to be.
tell us more about your bunny… you said the potty issue is better… that’s good. is she litterbox trained and not having any accidents in her cage?
is she a chewer or digger? if she’s destructive, you would probably need to address that first. have you bunny-proofed the area, and picked up or moved important things out of her reach?
is she spayed? spaying is very important for both the health of your rabbit and potty and other "bad bunny" issues tend to decrease.
i understand how frustrated you must be, but it is your parent’s house. they may have reasons they don’t want her out, so it would be best to talk to them, maybe get the issues they have on the table, and see if you can fix them or improve the situation for her another way.