:?:?:? Opening up websites yeah that takes up a bit of space, like a tiny tiny bit, Im not sure about youtube. I would expect that as it is streamed there wouldn't be much differrence between that and a 'normal' website.
but downloading is the major contributer to the problem you are having, you said you sister is downloading majorly. My OH downloads LOADS!! but we have never had a problem with being kicked off the internet for it.
ETA: we are with virgin media and have unlimited downloads, under a condition of "within reason":?