KVM with Caldigit TS4 - Should this setup work? What am I doing wrong?

Hello everyone. I’m hoping someone may be able to point out where I’m going wrong or what I need to do to get this setup working.

Here is a diagram of what I have going on:

My desktop works perfectly. My laptop on the other hand does not work at all. If I connect one of the monitors from the TS4 to the KVM using DP to DP, I can get that monitor to work but still no peripherals or the second monitor.

Any insight on what is going on here would be appreciated.

UPDATE: I’m able to get one display working of the two but no peripherals still.

UPDATE 2: I didn’t change anything, just power cycled the dock and the KVM. I now have 1 monitor and peripherals working. The second monitor still does not work though. Not sure what is going on with that.