Accessing your Linux computer from home

First, you need somewhat to have access to the CERN network. The suggested method is to use sshuttle.
If you use Gnome on your CERN desktop computer, a very simple way to get access to your screen is described on linuxhint.com. This is the easiest to setup and allows you to have control of your local X session.
Alternatively, a general tool is to use xrdp service which is probably available on any linux distribution. A possible guide is on digitalocean.com. However, this seems to be a bit more complicated to setup as one may wish.
From your home computer, you can use any remote desktop client (for windows, linux, mac) to access your CERN machine.

It might be that you then need to disable screen lock on your computer: this clearly is not particularly safe especially if you share your office with others.
There might be both gnome-screen-sharing service and xrdp running on your CERN computer: the latter, will prevent the first one to work!