Hello The Mute, I'm sorry to hear about that. Even though I can't particularly say I understand about THE distance BETWEEN you and your family. I can say that I am similar to you, at least at home.
When I am at home, I would lock myself in my room for extended periods of time. Doing homework, writing, and the occasional web search. But, I didn't feel like my family hated me. I also, don't think that being an introvert is the problem, just the individual. Because even though my habits are similar, I would still be invited by my family, and friends to gathering... And I was normally, the scared little rabbit in the corner of the room every time. :)
point being, it's the people, AND yes that includes YOU. your family has different people in it, mine does, and so the interactions are different. Your family probably feels that since you are by yourself often, you are comfortable like that. And you probably get nervous. my aunt, and my best friend thought that at first and that is why they didn't talk to me at first. BUT, the only thing I can agree with Eliaras is that you need to make an effort to interact more with people... I know that it may hurt a little to hear stuff like that, but I know from pasts experiences, and my own fear of interacting with people outside of school (not that you and I are the same way around people), has hampered my relationships.
I think Eliaras is right, if you want to see a change begin sitting down with your family at breakfast, even if they "forget you," try to insert yourself into family events.You will not know until you try.
Also, I used to feel like my family hated me too, and I still have a bit of a problem speaking to people without rambling or stuttering. So, I found that writing letters helps, you can get all your thoughts on paper and just plan out what you wish to say.
I'm telling you this, because I think that if this is the case, you need to discuss it. Otherwise you will constantly feel bogged down by your thoughts. I think You should try to sit your parents or the family, if you feel comfortable, and try to discuss your feelings. I recommend taking some time to think about your biggest concerns, then having the sit down. Try not to make accusations, as that will not solve anything, but try to state your feelings.
then work on compromising. I'm sure they could wake you up on occasion, but I think it will be best if you volunteer on occasion to participate with your family. Show them interest and they will do the same. Communicate instead of bottling things up, and you should be able to feel better.
I know it may be a little hard, but you never know unless you try.
I wish the best for you.