The persistent underrepresentation of women in engineering continues to be a complex and difficult challenge. The interactions of young women and their parents during early, family-oriented engineering design experiences can provide girls with opportunities to express agency during an engineering activity, which can ultimately contribute to the development of sustained interest and self-efficacy in engineering. However, few studies have examined these parent-child interactions to date, and none have specifically focused on moments when girls express agency during an engineering design process. In this paper, we examine one such setting: a museum exhibit that engages visitors in engineering design activity. A qualitative content analysis was performed on transcripts from a total of 39 family groups videotaped at the exhibit, each involving a daughter between the ages of 5-12 and at least one parent. Qualitative codes describing the ways children expressed agency and led interactions with their parents included "directing", "proposing design ideas", and "asking questions". Interestingly, the analysis also suggests that the young women in this study tended to direct their mothers more than their fathers. Although focused specifically on parent-child interactions, this study can inform both formal and informal engineering educators who engage young students in engineering activities.