If your power supply is the 19 volt laptop supply then it is already isolated. You can confim thet this is the case with the actual power supply you are using by measuring the resistance between its mains input and output with your meter set to the highest resistance range. To do this connect the 3 input wires together. (Live Neutral and earth.) Connect the Positive and negative output wires together then measure the resistance between the input and the output. There may be a low value capacitor between the input and output but this will only provide a path between input and output for high frequency noise. It would have a very high reactance at mains frequency. The only situation you would need your second isolation barrier is if this power supply was also providing power to a laptop and you wanted to provive isolation between your device and the laptop. (Or devices connected to the laptop via USB , serial or parallel ports.) (The network connector will be isolated by high frequency transformers in the laptop.)
Another way to provide an isolated power supply would be to use two permanent magnet motors coupled together and insulated from each other both at the mounting and coupling between the shafts. One would act as a motor the other would act as a generator.
Here is the drawing of the example situation to try to get you to understand the isolation voltage difference.

This is just an example. There are many situations where isolation is required. As you won't tell us what your situation is only you can tell us how much isolation you required.
Les.
Another way to provide an isolated power supply would be to use two permanent magnet motors coupled together and insulated from each other both at the mounting and coupling between the shafts. One would act as a motor the other would act as a generator.
Here is the drawing of the example situation to try to get you to understand the isolation voltage difference.

This is just an example. There are many situations where isolation is required. As you won't tell us what your situation is only you can tell us how much isolation you required.
Les.
