We present a vehicle system capable of navigating safely and efficiently around Vulnerable Road Users (VRUs), such as pedestrians and cyclists. The system comprises key modules for environment perception, localization and mapping, motion planning, and control, integrated into a prototype vehicle. A key innovation is a motion planner based on Topology-driven Model Predictive Control (T-MPC). The guidance layer generates multiple trajectories in parallel, each representing a distinct strategy for obstacle avoidance or non-passing. The underlying trajectory optimization constrains the joint probability of collision with VRUs under generic uncertainties. To address extraordinary situations ('edge cases') that go beyond the autonomous capabilities - such as construction zones or encounters with emergency responders - the system includes an option for remote human operation, supported by visual and haptic guidance. In simulation, our motion planner outperforms three baseline approaches in terms of safety and efficiency. We also demonstrate the full system in prototype vehicle tests on a closed track, both in autonomous and remotely operated modes.