Collaborative play not only provides entertainment but also nurtures connections and strengthens community ties. In family and intergenerational contexts, collaborative activities and play can engage family members in quality conversations and meaningful connections over distance. To explore participants' preferences, practices, and interaction dynamics when playing remotely, we conducted a design probe study with 15 groups of parents and children from 16 families. Our findings highlight both similarities and notable differences in the use of communication methods, workspaces, and objects between parents and children. Specifically, we observed distinct patterns in gestural and verbal communication and identified specific challenges encountered by children in a simulated remote setting. Our findings also revealed the dynamics of play sessions, particularly when co-located participants are involved, shedding light on the complexities of remote intergenerational communication and play. Our work contributes empirical insights into designing more effective and engaging remote collaborative platforms for families.