I'm not positive what the question is, but I'll try to throw out some information in hopes of saying something helpful.  There are ball valves which have three ports on them, one port is connected to one of the others, depending on which way the valve is turned.  These are used for things like a foamer where you want to switch from one side to the other.  I don't think this really fits your situation as I see it.  There are two port ball valves which have two wires, power applied in one direction will make the valve open, power applied the opposite polarity will make it close.  This is how the pressure controlling valve on your sprayer works, although it may be a gate valve instead of a ball valve.  In most cases the boom shutoff valve will be a three wire valve.  One wire is 12+, one is gnd, and the third is energized when you want the valve open and non-energized when you want it closed.  You will have to run the 12+ wire to the valves to make them work.  The signal wire will hook directly to where your solenoid valve is hooked. 

A ball valve is going to have an in and an out port.  You will have to supply them from a manifold made up of nipples and tees.  Alternatively,  Banjo sells a set of three ball valves already assembled onto a manifold with their flange type fittings.