What is the ruling on a daughter shunning her father who sexually assaulted her in the past, given that she hates him and does not want to communicate with him?

If your father committed a great evil, his right over you is not abrogated. For Allah has commanded companionship with parents in kindness, even if they enjoin shirk. Therefore, it is not permissible for you to completely sever ties with your father. If you dislike him because of his actions, there is no sin in that. However, this dislike should not prevent you from honoring him and maintaining ties with him, especially if he repents.