Existing novice-friendly machine learning (ML) modeling tools center around a solo user experience, where a single user collects only their own data to build a model. However, solo modeling experiences limit valuable opportunities for encountering alternative ideas and approaches that can arise when learners work together; consequently, it often precludes encountering critical issues in ML around data representation and diversity that can surface when different perspectives are manifested in a group-constructed data set. To address this issue, we created Co-ML – a tablet-based app for learners to collaboratively build ML image classifiers through an end-to-end, iterative model-building process. In this paper, we illustrate the feasibility and potential richness of collaborative modeling by presenting an in-depth case study of a family (two children 11 and 14-years-old working with their parents) using Co-ML in a facilitated introductory ML activity at home. We share the Co-ML system design and contribute a discussion of how using Co-ML in a collaborative activity enabled beginners to collectively engage with dataset design considerations underrepresented in prior work such as data diversity, class imbalance, and data quality. We discuss how a distributed collaborative process, in which individuals can take on different model-building responsibilities, provides a rich context for children and adults to learn ML dataset design.