Can I use a kvm AND a docking station?

What up y'all, I'm having trouble conceptualizing this and I don't know if it'll even work. What I need is two computers a gaming computer and a work laptop hooked up to the same screens but they both need a hard line connection. Since I can't figure out how to Google this problem I wanted to ask a bunch of super dorks on Reddit thier opinion. I haven't tested or done anything because it's going to affect what I buy for cable management so I wanted to see if anyone else has figured this out, or if I'm overthinking this. I appreciate any help / roasting you can dish out.

Hers and His setup (although query “his” headphones?)

First post since office reno!

Rate my shitty set up

Matte Black Setup

Trying to keep my setup as simple as possible.

Made Some Updates Since Last Time - trying to find a mic arm for my Blue Yeti but struggling with the aesthetic

Finished the station with a new chair. Now permanent till we move.

Many years we where laptop users. January we built a really nice PC, and decided to switch to a battle station. Bit by bit we found what we needed. 1970’s teachers desk from habitat for humanity RE store, Brother MFC-L27500W printer scanner, Edifer R1280DB with a mono price 6 inch powered sub driven by an AE-5 plus sound card, hyper X blue keyboard, Logitech G602 wireless mouse. Lenovo G34W-10 ultra wide. Just added a Staples Hyken chair, we where using a kitchen chair. Had to do the headrest mod, and need to make a riser yet. We finally are done untill we move to our next home. Wife does hybrid WFH, we both study, and I play games.

Took a lot of renovation but my final battle station! Super happy with it!

Built new PCs for myself and my fiancé.

We play almost everything together (besides dcs world 😅) she never had a gaming pc so I decided it was time to change that and upgrade mine as well at the same time.

My Little Happy Place

My home base