NOT RIGHT!
12 volt positive should NOT go to the valve from the battery.
The valve needs a ground.
12 volt positive for the valve should come from the switched (normally open) terminal of the relay
The relay needs a 12 volt supply to the common terminal of the relay. It should be protected, fuse or circuit breaker. It can be direct from the battery or from a source only "hot" with the key ON. As long as circuit choosen will support the amp draw of the valve.
The relay has a coil. When current energises the coil the relay switches the power to the valve. You need to get 12 volts across the coil of the relay. There are several ways to do that. If you want it to only work with the key ON you need to find a 12 volt supply that is only "hot" with the key on. You can then send this 12 volts to your joystick switch, from the joystick switch to the relay coil. Then gound the other side of the coil.
OR you can send this 12 volt supply to the relay coil, then from the other side of the relay coil go to the joystick switch, then from the other side of the joystick switch go to ground. This way may take less wire.