What are the rights of a son upon his mother who wrongs him and does not care, and how can one show piety to her despite the harm and hatred?

Being dutiful to one's mother is an obligation, even if she wrongs you, and her right does not fall away due to her mistreatment or injustice; because a person may not control love and hate, but they do control physical actions.

Among the things that help in being dutiful to one's mother are striving against one's own self, seeking Allah's help, purifying one's intention for His sake, and recalling the virtue and status of honoring parents, and the reward Allah has promised; for the Lord's pleasure is in the parent's pleasure, and His displeasure is in their displeasure, and the parent is the middle gate of Paradise.

Being dutiful to one's mother, in particular, is among the best acts of obedience, the quickest in reward, and the most hopeful for blessing in sustenance and lifespan.