Dexterous manipulation promises substantially richer robot interaction with the physical world, but learning these behaviours remains constrained by the difficulty of collecting consistent, complete-task demonstrations. Unlike parallel-jaw manipulation, dexterous tasks require the operator to coordinate arm motion with precise, contact-rich finger behaviour throughout the task. We introduce NestDex, a nested policy-learning framework that reduces this burden by using learned hand skills to assist demonstration collection. The operator controls the arm and regulates the active hand skill through a single-DoF clutch, rather than directly specifying the full finger trajectory. The inner hand policy adapts its motion from the latest proprioceptive history, while a vision-language selector activates the appropriate skill for each task stage. The resulting demonstrations train a separate outer visuomotor policy that controls both the arm and hand without the inner policies at deployment. A hand-action variational autoencoder provides compact hand-action targets while retaining arm commands in joint space. Across real-world dexterous manipulation experiments, NestDex improves demonstration reliability and efficiency, and the resulting empirical evaluations support effective autonomous policy learning. Video Demo are available at project website https://aus.bot/research/nestdex.

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