First off you'll most likely have to capitulate. If your using an internet connection you don't pay for then you have to allow the person that does pay for it to decide how it is used, ultimately it's their responsibility.
You don't say why she wants you to change the posts, but she obviously doesn't agree with what you're posting.
Perhaps you've given away more information about yourself or your family than she is happy with being available to the internet at large, which is perfectly reasonable.
If she is unhappy with the language you are using, such as swearing or vulgar slang, then maybe you can reach a compromise to rewrite the paragraphs with cleaner text. There are no good points that can't be made without vulgarity.
If it's that she doesn't agree with your opinions then you're probably going to have to sit on them. I'm guessing you're still early to mid teens and unfortunately, for a while yet, your parents are still responsible for you, and your actions and opinions still reflect upon them and how the rest of your family and their friends see them. Even if you don't agree with them, until you're responsible for yourself (i.e. paying the bills) it's a harsh truth that you might have to bite your lip to maintain family harmony.
In conclusion you most likely have to play by her rules, and the only option is to try to calmly reason your case with her and hope to find a happy compromise.
If you really feel like what you have to blog about HAS to be said, then you'll have to sneak out and use an internet cafe or other public connection, but you'd better be certain you've got unshakeable right on your side because sneaking and lying invariably gets found out and there's always a price.