U4320Q, PIP/PBP use the same mouse and keyboard

Hi everyone, 

I have just been delivered a brand new U4320Q 42.5'' screen and would like to use the PIP/PBP mode.

I have read through several of the chains here and already spoke to the customer service about this, but no help.

Right now I have my Latitude 5300 connected to the monitor using HDMI and another Microsoft Surface connected to the monitor using USB-C. the USB transmitter for the keyboard and mouse is connected to the monitor's left "upstream" (I believe that's what it's called) plug. 

I get the PIP/PBP to work, but my issue is that I would like to use only one set of keyboard and mouse. I have read about KVMs and honestly, I am a bit lost.

For some reason the mouse now only controls the Microsoft Surface and that's obviously just a small part of the screen. I would then have to either use the Latitude's mouse to move around the monitor on that part of the screen, or unplug the transmitter from the monitor and plug it straight into the Latitude.

I would really appreciate some help here. In advance: thanks a lot for everyone's help!