We introduce ArtInsight, a novel AI-powered system to facilitate deeper engagement with child-created artwork in mixed visual-ability families. ArtInsight leverages large language models (LLMs) to craft a respectful and thorough initial description of a child's artwork, and provides: creative AI-generated descriptions for a vivid overview, audio recording to capture the child's own description of their artwork, and a set of AI-generated questions to facilitate discussion between blind or low-vision (BLV) family members and their children. Alongside ArtInsight, we also contribute a new rubric to score AI-generated descriptions of child-created artwork and an assessment of state-of-the-art LLMs. We evaluated ArtInsight with five groups of BLV family members and their children, and as a case study with one BLV child therapist. Our findings highlight a preference for ArtInsight's longer, artistically-tailored descriptions over those generated by existing BLV AI tools. Participants highlighted the creative description and audio recording components as most beneficial, with the former helping ``bring a picture to life'' and the latter centering the child's narrative to generate context-aware AI responses. Our findings reveal different ways that AI can be used to support art engagement, including before, during, and after interaction with the child artist, as well as expectations that BLV adults and their sighted children have about AI-powered tools.