GPU-based simulation environments for embodied AI interleave physics simulation (CUDA) and photorealistic rendering (Vulkan) on a single device. We observe that two foundational scenarios -- simulation data generation and RL training -- can be naturally adapted to execute their simulation and rendering phases concurrently, presenting a significant opportunity to improve GPU utilization through spatial multiplexing. However, a fundamental obstacle we term execution isolation prevents this: CUDA and Vulkan create separate GPU contexts whose channels are bound to different scheduling groups, confining compute and graphics to mutually exclusive time slices. Existing spatial-sharing techniques are limited to the CUDA ecosystem, while temporal-sharing approaches underutilize available resources. This paper presents VUDA, a system that breaks execution isolation to enable spatial parallelism between CUDA compute and Vulkan graphics workloads. VUDA is built on two key observations: although CUDA and Vulkan expose different programming abstractions, their execution paths converge to a common channel primitive at the driver and hardware level; meanwhile, their virtual-address spaces are inherently disjoint, making safe page-table merging feasible without remapping. VUDA exposes a thin API for developers to annotate co-schedulable CUDA streams, and realizes spatial sharing through channel redirection into Vulkan's scheduling domain and page-table grafting to unify address spaces, eliminating all data copying on the critical path. Experiments on representative embodied-AI workloads show that VUDA delivers up to 85% higher throughput than temporal-sharing baselines, while improving GPU utilization and reducing end-to-end latency.