What should a girl do who has been engaging in sexual activity with her brother since the age of ten and desires to repent, but her brother forces her to continue? How can she rid herself of this sin? And what is her religious obligation?

What occurs between a young man and his sister, of engaging in anal sex, is zina (fornication/adultery) and is a grave major sin. Zina with a mahram (unmarriageable kin) is even more strictly forbidden, because mahrams are obligated to protect honor, not violate it. She must repent with a sincere repentance and conceal herself with Allah's concealment, and not tell anyone about her past. For Allah accepts the repentance of those who repent and transforms their bad deeds into good ones, and "the one who repents from sin is like one who has no sin." It is incumbent upon you to inform her of this fatwa and help her remain steadfast on her new path, and to conceal her and not inform anyone of her matter.