Whatever the solution employed is, it has to be a third device additional to the 2 QLab computers to provide dual triggering that is not reliant on both machines being functional.
The cheapest is a MIDI GO box style remote with 2 parallel MIDI outputs. If you need lots of buttons for a non linear show, a MIDI keyboard (with a standard MIDI output socket) split with a MIDI thru box would give, you up to 88 buttons (keys) which are completely silent in operation and very reliable.
If you don't need tactile feedback a device running TouchOSC (preferably wired, through an ethernet adapter), can send any number of MIDI or OSC messages to multiple destinations, from as many buttons as you can safely cram onto the display of the device.
If you need to use Companion then it would need to run on a third device, and the cheapest device, is likely to be a raspberry pi.
All the above solutions can be reliably achieved with readily available equipment for between 100-200 pounds/dollars.
Mic