Robotic assistance in scientific laboratories requires procedurally correct long-horizon manipulation, reliable execution under limited supervision, and robustness in low-demonstration regimes. Such conditions greatly challenge end-to-end vision-language-action (VLA) models, whose assumptions of recoverable errors and data-driven policy learning often break down in protocol-sensitive experiments. We propose CAPER, a framework for Constrained And ProcEdural Reasoning for robotic scientific experiments, which explicitly restricts where learning and reasoning occur in the planning and control pipeline. Rather than strengthening end-to-end policies, CAPER enforces a responsibility-separated structure: task-level reasoning generates procedurally valid action sequences under explicit constraints, mid-level multimodal grounding realizes subtasks without delegating spatial decision-making to large language models, and low-level control adapts to physical uncertainty via reinforcement learning with minimal demonstrations. By encoding procedural commitments through interpretable intermediate representations, CAPER prevents execution-time violations of experimental logic, improving controllability, robustness, and data efficiency. Experiments on a scientific workflow benchmark and a public long-horizon manipulation dataset demonstrate consistent improvements in success rate and procedural correctness, particularly in low-data and long-horizon settings.