Here are another two videos by Michael Brown,
Have a look at all 4. Michael explains what you are trying to do with several options for your second screen but you need to network both computers when running both copies of X-plane. By running the panel on the second computer it is advisable to "dumb down" the computer just running the instrument panel. Michael explains this.
I can't remember which video has the best solution you are seeking. I intend to initially run the second copy on another hard drive (my hangar drive) before I acquire a second computer. Michael also explains this as well which is his preferred option.
Once you have the second screen operational, press Ctrl-W for the computer running the visuals. This will clear your screen of the instrument panel allowing you to run the instrument screen.
Others on this forum have also asked the same question you have raised and the answer supplied from, generally "jroberts", is "network and run a second version on another computer".
Hope this helps further.