Is a father's continuous prayer against his daughter and wife answered, and is the daughter sinful for disliking her father due to his bad treatment?

If your father is aware of his actions, he is accountable for them. His accusation of your mother committing zina (fornication/adultery) is a grave slander, one of the major sins. Similarly, insulting, cursing, and unjustly invoking evil upon him are reprehensible acts. We advise you to be patient with him and supplicate for him. Assign someone to advise him and clarify the gravity of his actions to him, as his position as an imam of a mosque further exacerbates the ugliness of his deeds. Filial piety towards him is obligatory and his misdeeds do not negate it. Your keeping a distance from him to avoid his harm does not contradict filial piety. There is no harm in disliking him because of his actions, but be careful not to let this lead to ill-treatment of him, for disobedience to parents is one of the destructive sins. If his supplication against you is unjust, we hope it will not be answered, but beware of a parent's supplication.