Once you get everything set ky up this way. Let me know if you need further help I did copy and paste this from a post I was helping someone on PO with it awhile back.
You can do it another way where you don't clone 1 with 3 and just have monitor 1, monitor 2 (if you have an extra monitor), and then elgato. In this case you would capture the screen 3 (Elgato) via your streaming pc via capturing it -> Video Capture Device -> Elgato.
My setup