A system for remotely controlling hydraulic component of an agricultural implement towed by a work vehicle may include a vehicle-based valve assembly that selectively supplies hydraulic fluid to one or more supply lines of the implement. Specifically, a first supply line may be fluidly coupled to an implement-based valve assembly that regulates the supply of hydraulic fluid to a hydraulic actuator through a first actuator line. A second supply line may be fluidly coupled to the first actuator line downstream of the implement-based valve assembly such that when a user provides a control input at a remote interface, the vehicle-based valve assembly may instead regulate the supply of hydraulic fluid to the actuator. The supply of the hydraulic fluid through the supply lines may additionally be controlled by first and second override valves fluidly coupled to the first and second supply lines, respectively.