From what you have listed both your monitors have VGA input
Only one monitor has Hdmi input
You need a switch with 2 vga out OR 2 HDMI out and a hdmi to vga converter.

Your current switch only has 1 out so it can only do one monitor.
See what I can find,
@Gr3iz @Couriant

 

Is this the KVM you have?

As Peter points out, one of your monitors is VGA only. Also, with the desktop only providing 1 HDMI and 1 VGA, the extra conversions required are just asking for trouble. The dock is OK, DP to HDMI adapters are easily sourced.

It would appear you'd need something like this (and I am not endorsing, nor recommending it, just pointing out the type of KVM that looks like it would work for your situation):
https://www.amazon.com/Extended-CKL-Keyboard-Selector-Computers/dp/B07YZ6RPTV?th=1

 

Thank you, Peter and Gr3iz. I haven't had a chance to work on this the last couple of days but I wanted to acknowledge your responses. I appreciate the information you have provided.

Yes, Peter, that is the KVM that I have. Hopefully, I will be able to work on this over the weekend.

Thank you both again!

 

Keep us posted.

 

I have 3 dual monitor HP desktops running 3 Monitors.
I'm using a combination of these KVMs
And Two display port to VGA adapters (for the newer HPs)

The second monitor Must be connected when booting if it normally has anything being displayed.
You'll have to experiment to see which KVM defaults to Connected at boot.

 

I want to thank everyone again! I have been able to get everything set up and working correctly. I've been using the setup for a couple of weeks with no issues.

I ended up getting the Dual HDMI & VGA KVM switch. With that KVM switch and two VGA-to-USB adapters, I connected the PC and laptop to my two monitors, mouse, keyboard, sound, and printer.

 

Excellent! Glad to hear it!

You can mark your thread "Solved" if you are satisfied.