Docking Stations USB-C Switching with Networking

I'm looking for a solution that will allow me to switch between two laptops using USB-C output from the two laptops to 1 set of monitors, 1 keyboard, and 1 mouse, AND, this is the tricky part, I need the switch to also switch Ethernet cables so that one laptop goes to 1 port on my firewall and the other laptop goes to another port on the firewall...BUT...I don't want to run network cables to the laptops. I want the laptops to connect to the switch with the USB-C only and then the switch handle the KVM switching AND the network switching. Not sure if this is possible, but that is what I am looking for.

One laptop is business and one is personal; the business laptop will be hardwired via Ethernet to a specific port on the firewall that has a VPN connection to my office; the other laptop will be hardwired via Ethernet to go straight out to the Internet. I have it drawn out.

 

I think I figured out the only solution. I need to place 2 USB-C docking stations with ethernet out ports between the laptops and the KVM switch. That will separate the network switching from the KVM. Each USB-C dock will take in the USB-C from the laptop, then output the ethernet cable to the firewall and the HDMI and USB-A to the KVM. I doubt there is a single device that will do all of this in one device.