Robot teleoperation enables safe, non-contact task execution in hazardous environments where direct human access is difficult, and its application has expanded with recent VR technologies. Many VR teleoperation studies, however, have primarily served as data-collection tools for robot imitation learning, so they often do not explicitly address dynamic obstacles, workspace changes, or collision risks during operation. For real deployment aimed at operator safety, teleoperation must react to dynamic situations with low latency and remain robust to mistakes made by inexperienced operators. This paper presents a VR teleoperation framework that supports real-time manipulation while handling collisions with both static and moving obstacles. The framework integrates GPU-accelerated inverse kinematics and trajectory optimization within a VR interface to generate feasible joint commands at each control cycle under robot constraints. Experiments with a 7-DoF manipulator demonstrate stable online behavior and collision-aware motion generation across three scenarios: obstacle-free, static-obstacle, and moving-obstacle environments. The results indicate that the proposed approach generates motion consistent with the operator's command while producing safe detours when obstacles interfere with the commanded path.