Autonomous free-flyers play a critical role in intravehicular tasks aboard the International Space Station (ISS), where their precise docking under sensing noise, small actuation mismatches, and environmental variability remains a nontrivial challenge. This work presents a reinforcement learning (RL) framework for six-degree-of-freedom (6-DoF) docking of JAXA's Int-Ball2 robot inside a high-fidelity Isaac Sim model of the Japanese Experiment Module (JEM). Using Proximal Policy Optimization (PPO), we train and evaluate controllers under domain-randomized dynamics and bounded observation noise, while explicitly modeling propeller drag-torque effects and polarity structure. This enables a controlled study of how Int-Ball2's propulsion physics influence RL-based docking performance in constrained microgravity interiors. The learned policy achieves stable and reliable docking across varied conditions and lays the groundwork for future extensions pertaining to Int-Ball2 in collision-aware navigation, safe RL, propulsion-accurate sim-to-real transfer, and vision-based end-to-end docking.