Sharing family stories is an integral aspect of how families remember together and build a sense of connection. Yet, when generations in families are separated by large geographic and temporal distances, the everyday taken-forgranted processes of sharing family stories shift from conversational to mediated forms. To inform HCI research and practice in mediating family stories, we contribute an account of the co-constructive intergenerational social practices enacted to co-construct and interpret family stories. These practices demonstrate the agency of both storytellers and listeners as they work to discover, decipher, and reconstruct family stories. We close by drawing insights from this setting to frame key design challenges for multi-lifespan information systems mediating asynchronous, asymmetric, co-constructive and socially weighted information sharing interactions.