Caregivers (i.e., parents and members of a child's caring community) are underappreciated stakeholders in learning analytics. Although caregiver involvement can enhance student academic outcomes, many obstacles hinder involvement, most notably knowledge gaps with respect to modern school curricula. An emerging topic of interest in learning analytics is hybrid tutoring, which includes instructional and motivational support. Caregivers assert similar roles in homework, yet it is unknown how learning analytics can support them. Our past work with caregivers suggested that conversational support is a promising method of providing caregivers with the guidance needed to effectively support student learning. We developed a system that provides instructional support to caregivers through conversational recommendations generated by a Large Language Model (LLM). Addressing known instructional limitations of LLMs, we use instructional intelligence from tutoring systems while conducting prompt engineering experiments with the open-source Llama 3 LLM. This LLM generated message recommendations for caregivers supporting their child's math practice via chat. Few-shot prompting and combining real-time problem-solving context from tutoring systems with examples of tutoring practices yielded desirable message recommendations. These recommendations were evaluated with ten middle school caregivers, who valued recommendations facilitating content-level support and student metacognition through self-explanation. We contribute insights into how tutoring systems can best be merged with LLMs to support hybrid tutoring settings through conversational assistance, facilitating effective caregiver involvement in tutoring systems.