Parent-AI collaboration to support real-time conversations with children is challenging due to the sensitivity and open-ended nature of such interactions. Existing systems often simplify collaboration into static modes, providing limited support for adapting AI to continuously evolving conversational contexts. To address this gap, we systematically investigate the dynamics of parent-AI collaboration modes in real-time conversations with children. We conducted a co-design study with eight parents and developed COMPASS, a research probe that enables flexible combinations of parental support functions during conversations. Using COMPASS, we conducted a lab-based study with 21 parent-child pairs. We show that parent-AI collaboration unfolds through evolving modes that adapt systematically to contextual factors. We further identify three types of parental strategies--parent-oriented, child-oriented, and relationship-oriented--that shape how parents engage with AI. These findings advance the understanding of dynamic human-AI collaboration in relational, high-stakes settings and inform the design of flexible, context-adaptive parental support systems.

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