Remote play an epic games game.

[Dreams]

So this one is a doozy. I own Borderland 3 Through epic games. I've already figured out that you can use the steam client to play non-steam games remotely, through steam link/remote play if the drm is loose (windows store games for example). Well epic games drm is not, so it will not allow steam to launch the game, it has to be launched through epic or the shortcut. Well I solved that, I created a batch file that launches it properly, then I converted that to an executable, and added it to steam as a non-steam game. That actually worked, I can now launch BL3 using the play button in steam. This also allows me to "stream" it on my laptop logged into the same account which is my ultimate goal. The problem is it doesn't actually display the game. On steam link on my phone, I can minimize Big Picture and just click the program with the touch screen moving the cursor as it mirrors the whole desktop. This isn't the case for pc to pc remote play, its just supposed to autodetect the window and because it launches epic games first, then BL3, it doesn't detect properly. So I want to know how to get it to mirror my whole desktop like steam link, or how to switch which window it focuses, or any other work around you can think of. It's very annoying I can play it on my phone, and with a little more work on my tv, but not on my laptop (the perfect screen size for my situation). I want to add than an android emulator and the steam link app within it isn't realistic, as the latency is amplified on top of what already exists.

tl;dr: How can I change the focused window when streaming a game from my desktop to my laptop, or mirror the whole desktop similar to steam link, without getting an android emulator to get the steam link app on a pc, as that has latency issues?