A device and method of handling a plug in a tubing hanger includes a pressure actuated sequence valve that has multiple outlets. Hydraulic fluid from a remotely operated vehicle (ROV) provides hydraulic fluid that selectively flows through the valve for operating a tool that handles the plug. The valve outlets are ported to separate lines for operating different functions of the tool. Flow to a specific outlet occurs by sequencing the valve to a corresponding position, where the valve is sequenced by changing pressure of the hydraulic fluid. The sequence valve is disposed in a piston that is axially movable within the tool. A stroking rod attaches to the piston, and is actuated by diverting flow to sides of the piston.