Would sending Ramadan greetings only to an aunt, without speaking to her after the psychological harm she caused and her refusal to admit fault, be considered a sin for which God would hold one accountable, and would God be displeased with the questioners for their inability to forgive her despite their mother maintaining ties of kinship?

Maintaining kinship ties (Silat al-Rahim) is obligatory, and severing them is forbidden and considered one of the major sins. The maternal aunt is like a mother, and she is among those relatives most deserving of being honored and maintained. Her failure to assist you in times of hardship does not permit severing ties with her; rather, the obligation is to maintain ties with her kindly. Maintaining kinship ties can be done through financial support, fulfilling needs, visiting, writing, sending greetings, and any act that is customarily considered a form of maintaining ties. Maintaining kinship ties has a great reward, expands sustenance, and prolongs life.