Solid-state relay - Integration in circuit
I don't see how you would use the SSR in the position you suggest. Opening up that input is not the same as making the voltage 0V. 

You should note that the SSR needs something like 5mA through the LED to switch 'on' reliably, so make sure that whatever drive circuit you are using is supplying sufficient current. 

Maybe you could increase the 1 ohm sense resistance, depending on your range of load resistances.

Edit: I'm changing the suggestion because there was a path I didn't notice before the coffee. 

Put the SSR output between the + input of the op-amp and ground. You could also use a small MOSFET such as a 2N7000 or (better) a TN0104  instead of the SSR and drive it directly from the RPi.