Being able to retain LiveView in both your Camera and on your Laptop at the same time

I don't think this is possible [though I'd love to be proven wrong].

I'd think of it in the same way as trying to drive two monitors from a low-end graphics card. One screen, fine; two screens, no, not even in mirrored mode.

With the following setup I am able to see LiveView simultaneously on my laptop and on my camera:

• Canon 550D
• USB connection
• Windows 10 version 1909
• EOS webcam utility 1.0 for the 600D

I understand this is not a Nikon, but I wanted to post this answer to note that it's not an inherent DSLR limitation.

Perhaps you can try and connect your camera via the Nikon Webcam Utility (the Nikon equivalent of the EOS webcam utility) and see LiveView on both your camera and laptop.

You can connect the HDMI output to a separate monitor or computer and have live view displayed on both. This is useful for better detailed preview, letting clients see what's going on, or for educational uses. I'm pretty certain this works with every Nikon that has HDMI output.

But, if you also connect USB for tethered control or file transfer then the HDMI output is disabled; the work around for file transfer is wifi (card/adaptor) or ethernet on some models (D4/D5).

There is also NikonHacker that can enable some additional features/functions for some cameras; and clean HDMI w/ live view for the D5100 is one of the functions... but I have no personal experience w/ it.