Bram, if your question was for Damien's specific setup, then ignore the rest of this.
For my mount, I can definitely have multiple machines connected as well as the hand controller. The mount is accessed via ethernet (wifi normally), so any machine that can connect to it, can control it.
Before I got my new laptop, I ran a small netbook at the mount for guiding (plus camera control, etc). However it wasn't powerful enough to plate solve, so I used my desktop machine in the house to plate solve and slew the telescope on results. And, of course, from Stellarium as well.
This worked even if I was guiding and then forgot to turn it off before slewing to another target. The mount just seemed to take the commands in turn. Mind you, when the slewing starts PHD rightfully goes nuts and stops trying to guide anyway.