Children grow up fast. Many parents want to capture the candid, fleeting moments of their young children's lives to treasure later, but these moments are difficult to anticipate and to capture without disruption. Current technologies to address this are limited to indiscriminately capturing everything, or are dependent on parents' presence and prescience to initiate capture and manually record the moment. To address these limitations, we introduce KidKeeper, a toy-like system to capture, select, and deliver everyday family memories with minimal effort and disruption to family life. It uses an innovative approach to capture that we call "integrated capture," that combines previous attempts to continuously capture family memories with the practice-oriented approach of "unremarkable computing" to embed capture capabilities unobtrusively into everyday activities. In our study, we explore how technologies like KidKeeper mediate and align the different interests and values of various family members, namely parents who want precious moments and children who want to play, towards accomplishing a family goal to capture memories of everyday life.