An assembly is used with a remote source of hydraulic power to control flow of wellbore fluid in a drilling system. At least one choke is operable to control the flow of the fluid to other portions of the system. At least one hydraulic actuator disposed with the choke actuates operation of the choke in response to the hydraulic power. At least one control valve disposed with the choke controls supply of the hydraulic power to and controls return of the hydraulic power from the actuator. An accumulator can be disposed with the choke and coupled to the supply upstream of the control valve. The control valve can couple to the actuator with a pair of pilot-operated check valves disposed in fluid communication between the control valve and the actuator. A stage tank and stage pump can be disposed with the choke. The tank receives the return from the control valve, and the stage pump can pump the return from the stage tank to the source.