Is informing one's sister about the hurtful actions of a distressing partner, which cause distress, considered backbiting (gheebah) or calumny (nameemah) that necessitates sin, especially given that the sole aim is to alleviate distress?

Informing your sister about a woman's mistreatment of you is forbidden backbiting, unless it is for a legitimate Sharia (definition) purpose, and not merely to relieve anger. This woman should be advised with wisdom and gentleness, or threatened with informing someone who can restrain her if she does not benefit from the advice. You should also strive to avoid associating with this woman if she is harmful; for a graceful avoidance may be better than a harmful association. It is permissible to avoid someone for more than three days if associating with them brings religious or worldly harm.