Your parents are just bullshiting you. They just don't want you to read all night long and instead go to sleep. When I was living with mine, they tried to pull the same shit. As for your night time reading, there are few ways to do it. One - get an adjustable light switch. Just turn your lights down to a degree where you can still read, but it won't leak out that much. Two - you can get something like Philips Hue bulbs, this way you can adjust lights without the need to change switches. Three - an led clip, attachable to a book Four - a modern LED lamp, such as this Five - a reading led that you place on the page. This crap: Not sure how well this will work Six - buy an e-book reader and switch to reading ebooks. You can sometimes get ebook versions either free or with a significant discount if you own a hard copy. With an ebook reader there won't be a need for lights.
First off, like many had suggested, I'd do something about the gaps around the door if I were you. Rather than using rugs or towels (please don't, they're not meant to be used like that @@ ), if you look into the house insulation section in a hardware/houseware store near you, I think you should be able to find either foam or rubber strips that sticks around either your door or the door frame. Those aren't expensive, and should save you (or your family) a few extra bucks of power bill as a bonus. And then, make sure that the light you intend to use for night reading is diffusive rather than directional/focused, and (from experience) the best position to do your reading is actually one of the corners closest to the door, with the diffusive light source pointed in the general direction of that corner. The catch with the directional lighting is that, though the light will go in the direction you point your lamp to, the spot where the focused light shines on effectively becomes a secondary light source, which may just be enough to attract attention of your folks. Though if all else fails, you can either train your ears to catch the slightest of sound and turn off the light as they approach, or you can simply pull a small lamp inside your bed cover and read in there. XD