Child speech differs from adult speech in acoustics, prosody, and language development, and disfluencies (repetitions, prolongations, blocks) further challenge Automatic Speech Recognition (ASR) and downstream Natural Language Processing (NLP). Recent large audio-language models (LALMs) demonstrate strong cross-modal audio understanding; however, their behavior in disfluent child speech remains underexplored. We evaluate several state-of-the-art LALMs in two settings: an interview (mixed speakers) and a reading task (single child). The tasks are (i) single-channel source separation to isolate the child and (ii) child-only summarization that preserves clinically relevant disfluencies and avoids adult-speech leakage. Evaluation combines Large Language Model (LLM) as a judge, human expert ratings, and BERTScore (F1), and we report agreement between models and between models and humans to assess reliability. Our findings delineate the conditions under which LALMs produce faithful child-only summaries from mixed audio and where they fail, offering practical guidance for clinical and educational deployments. We provide prompts and evaluation scripts to support replication.