container on same network with host
I could have mentioned this in comment first but I need 50 reputation to comment and I just joined this yesterday,

So, may I know what you are trying to achieve? If I interpret correctly, you want to move your VMs to Docker and then make those docker interact with each other as well as with graphics which is running on host? So consider it this way, you have 4 IP addresses, how would you make the communicate if it is simple LAN? Similarly you do it here. Allow hosts from that IP to work here. 
You can customize docker0 bridge to have gateway and CIDRs of your choice by modifying daemon.json

Customize the Docker0 bridge

You can create your user defined networks too.

May be this will help you too?
Docker Networking User Guide

You can even write your own network plugin.