What is the ruling on supplicating against a paternal cousin's daughter who psychologically and verbally abuses her maternal aunt's daughter in front of others, and has caused her family problems?

It is not permissible for a woman to despise you. She should be reminded of the impermissibility of this and assistance should be sought from those of sound judgment and wisdom. She should also be reminded of the Almighty's saying: "And do not call each other by offensive nicknames" [Quran 49:11], and the Prophet's (peace be upon him) saying: "Pride is disdaining the truth and despising people."

If she repents, then praise be to Allah. If she persists, then it is permissible to abandon her, based on the saying of Ibn Abd al-Barr: "They (the scholars) have unanimously agreed that it is permissible to abandon someone for more than three days if speaking to them brings a deficiency upon the speaker in his religion, or harm to himself or his worldly affairs. For often, a beautiful abandonment is better than a harmful association."

It is permissible to supplicate against her to the extent of her injustice. However, it is better to forgive, overlook, and repel with what is better, as the Almighty said: "But indeed, whoever perseveres patiently and forgives, that is [truly] of the matters [requiring] determination" [Quran 42:43], and "and those who restrain anger and who pardon people – and Allah loves the doers of good" [Quran 3:134]. And the Prophet (peace be upon him) said: "Allah does not increase a servant who pardons except in honor."