Well, I'm not sure if this will help, but I've been trying to do something similar with my tablet. I want a touchscreen monitor to try out the windows 10 touch features, but I don't have one, nor do I want to buy one.
I found that with my laptop, I can "Force" windows to see an external monitor that isn't actually plugged in, thus creating a second desktop that isn't displayed.
From there, I use Splashtop (or similar) to do remote desktop from my laptop to my tablet. Then I set it to show that secondary monitor on the tablet. This way, that extra screen space is shown only on my tablet, with all the touch features (well, almost).
So if you can force your computer to see another monitor that isn't there, you can broadcast THAT screen to your laptop, thus using your laptop as more monitor space.
The problem I'm running to, at least for NVIDIA desktops, is that I can't actually "force" it to see another monitor. It works just fine on my laptop, perhaps because of Intel drivers or maybe laptops don't even check for display presence.
But I guess that also depends on what you want to use the extra screen space for. I doubt you would be gaming on it, and CAD software might have an issue, depending on the remote desktop software you use. But otherwise, I think that's your best bet, especially if you don't have the budget to get some clunky video recording hardware that costs your wife and firstborn.