What should I do regarding my mother and my two aunts, who are quarreling over trivial matters, despite their refusal of external intervention, and the older aunt's unwillingness to visit her younger sister, even though the latter is keen on maintaining contact?

Your duty is to maintain ties with your two maternal aunts and other relatives, for upholding kinship ties is obligatory and severing them is a sin. Part of upholding these ties is to attempt to reconcile your mother and your two maternal aunts and their relatives, and to admonish whoever among them severs ties.