Using a Dell WD19 dock with two Dell laptops

I have two Dell laptops, both with a USB-C jack.  I connect my WD19 dock to one laptop and then I can use the two monitors, keyboard, mouse, USB devices, and network connection that all feed through the WD19.  That works great.

What I would like to be able to do is to disconnect the WD19's USB-C from one laptop, plug it into the other laptop, and have all of the peripherals and the network work with the other laptop.  That largely works, but not entirely.  There's two problems.

1) After the swap, the network seems congested or non-responsive.  If I reboot the second laptop, network responsiveness recovers.

2) After the swap, the second laptop often doesn't want to wake up after a mouse jiggle or a Ctrl-Alt-Del on the keyboard.  Sometimes it does, but other times what is required is an unrepeatable random walk through possibilities (mouse jiggle, key press, open clamshell and shut it, unplug dock and plug back in, followed by mouse jiggle, etc., etc.)

What I'd like to tell the dock is to flush everything and work with the second laptop.

What doesn't work:

- pressing the button on the dock

- rebooting a laptop each time I swap (I need the first laptop to stay in its same state when I switch to the second laptop

- combining both laptops into one laptop

- flushing the network cache on the second laptop

- using a KVM switch