Growing up, my mom was very strict when it came to anime. She wouldn't even let me watch Pokemon at the time. She was convinced that I would end up killing somebody by watching anime. In her opinion, it was too violent. As if I could suddenly call upon unnatural forces and shoot a fire beam at somebody. After I became an adult though, she couldn't do anything about it. She eventually stopped trying to control me because she knew she couldn't, and slowly I was able to convince her to like anime. She won't watch it, but she loves it when I talk to her in Japanese.
I really don't know what your parents are like Cherry-chan so I can't say that they'll grow into it like mine did, but hold it out and you won't be living with your parents forever. Just keep reminding yourself that. You have 5 more years before you become 18, and trust me, though it seems like a very long time from now, look at it in my perspective. It seems like yesterday that I applied for college, and I'm already in my 4th year. Time goes by fast.
Also, when times are tough, I just say my favorite saying from Card Captor Sakura, Nando Coladio Zettai Daijobou Daioh! (I'm sure something good will come from this! Everything will definitely be alright!) Remember that! It always works for me!