WD19DCS compatibility

Apologies if this isn't the appropriate spot for this post, as it's the closest I could find in terms of products that were relevant.

I was just given a Precision 7670 through work, which came with the WD19DCS dual USB-C dock. I'm trying to determine if or how I might be able to "swap in" my old HP Pavilion 15-cs0064st. The HP USB ports are data only, so I know I won't get video or power - it's more about not having to swap out the keyboard/mouse receiver and network cable every time I want to swap laptops.

I was previously using the regular WD19, which worked great for swapping in the old laptop, but I've had no luck connecting the DCS dock using either of the two USB-C from there.

So, I'm wondering if:

• I truly can't just connect the HP using one of the two options from the DCS dock, and if I can, what am I missing?
• If I can't use the DCS with the HP, can I "daisy chain" the two docks, where the WD19 has the ethernet and keyboard/mouse receiver, and connect that dock to the DCS to do some form of "pass through"
• Could I use the USB-C on the DCS to connect to the standard USB-A as a form of pass through for the data pieces from the dock?

Or, am I just toast and really just need to buy a separate "hub" that handles the receiver and ethernet, and swap those out as needed?

Thanks for any comments/thoughts/suggestions.