Must I constantly call my sisters to please my mother, despite being busy with my infant daughter and my home, and my weekly visits to my family, and my mother's anger at my not continuously communicating with my sisters?

Maintaining kinship ties is obligatory, and severing them is forbidden. Kinship ties are maintained through visits, communication, and gifting. What the sister does by visiting her sisters every Friday is considered maintaining kinship ties, unless custom dictates otherwise. The sister must obey her mother's request not to visit her sisters, unless it is beyond her capacity or leads to dereliction in her marital duties or other obligations, for Allah's pleasure is found in the pleasure of one's parents.