An active colloidal fluid composed of self-propelled spinning particles injecting energy and angular momentum at the microscale demonstrates spontaneous collective states that range from flocks to coherent vortices. Despite their seeming simplicity, the emergent far-from-equilibrium behavior of these fluids remains poorly understood, presenting a challenge to the design and control of next-generation active materials. When confined in a ring, such so-called polar active fluids acquire chirality once the spontaneous flow chooses a direction. In a perfect ring, this chirality is indefinitely long-lived. Here, we combine experiments on self-propelled colloidal Quincke rollers and mesoscopic simulations of continuum Toner-Tu equations to explore how such chiral states can be controlled and manipulated by obstacles. For different obstacle geometries, three dynamic steady states have been realized: long-lived chiral flow, an apolar state in which the flow breaks up into counter-rotating vortices, and an unconventional collective state with flow having an oscillating chirality. The chirality reversal proceeds through the formation of intermittent vortex chains in the vicinity of an obstacle. We demonstrate that the frequency of collective states with oscillating chirality can be tuned by obstacle parameters. We vary obstacle shapes to design chiral states that are independent of initial conditions. Building on our findings, we realize a system with two triangular obstacles that force the active fluid toward a state with a density imbalance of active particles across the ring. Our results demonstrate how spontaneous polar active flows in combination with size and geometry of scatterers can be used to control dynamic patterns of polar active liquids for materials design.