Analog 0...10V signal splitting
That solution of using opto-coupler wouldn't work for your problem if &quot;linearity&quot; matters in your system. The input resistance of SINK and MONITOR seems quite high enough, but their input capacitance might have caused the problem of delayed rising.
Anyway, your problem most likely will be solved if you use an Analog Buffer (which is linear). The simplest circuit to do that is to use an Emitter-follower as a buffer. You should connect the output of the Source unit to the input of this buffer and connect the output of buffer to your monitoring system. However, there's a problem that you have a 0.6v drop in your voltage through the emitter-follower buffer.

A more accurate analog-buffer can be implemented by an OPAMP. The advantage of using an Opamp-buffer is that its input impedance is pretty high, its output impedance is pretty low and there's no voltage drop across it.