Talk to your parents, calmly, and explain the situation in term they will understand. She is paying to get to use the connection, not to hog all the traffic. If they don't care, get a router where you can limit the speed and set hers to less than half of what you're paying for (since she's only paying 9 of the 30 euros). If that's not an option for some reason (I don't see why it wouldn't be, but just in case) unplug the damn cable every time she slows your internet down to being unplayable. If she complains, tell her she overloaded the router.
Trying to reason with someone like her will most likely not work, you'll just put yourself completely at her mercy. It's your home, you shouldn't have to do that. I've had a similar problem on a shared network in a student apartment, and talking to people did absolutely nothing. They nod and say they understand and then they do their own selfish thing again. Try progress raiding while someone's blocking your connection so badly you keep disconnecting. When you start hitting them with consequences when they act like jerks, that's when they start paying attention.