With the very small tool
x2x you can move your mouse to the left edge of your local screen and will continue to move over to the remote desplay. Your keyboard works on both computers as well, and you can even copy-paste between the two computers. It looks like the two computers got united.
At first you have to install x2x on the computer where you want to execute it (in the first possibility the remote one, in the second setup the local one).
I recommend to use x2x over a secured connection to any X-server in your network via SSH:
ssh -X 192.168.100.80 x2x -west -to :0
or (less secure):
Run the following command on the computer where you have a display attached (let's assume it has the IP 192.168.100.2), to allow 192.168.100.1 to connect to the X session:
And on the computer where your mouse and keyboard are attached run:
x2x 192.168.100.2:0 -west