Right! I remember having trouble with sound trough RDP with my servers as well, a while back. It's a pretty lame limitation by MS. So, RDP is probably out of the question then. VNC might be an option. I had to drop it after a few tests. The latency if way to high. That was a couple of years ago though.
You MIGHT have better luck if you set up some zones on the server it self, and connect the clients through each zone? There will be some wiring, and I do not really know how zones work. But something like this should be possible.
Probably not what you want to hear, but the option I find working best is to purchase cheaper small HTPC's as each client, and control the devices with remotes or touch screens. Each client connecting to the main library server. And/Or using android/OSx/win7&8 devices to connect to the library server though through the many options for DLNA playback and what not. It would probably cost more, but might give you less headaches.
Sorry. Wrote all this before I read about the Weblobby and transport controls. I'll leave it just in case you find it the slightest useful.
MC can be controlled trough remote commands and a web interface API. So, if Weblobby are customizable, you might be able to add MC control to this one. Or adding weblobby control to a customized webgizmo page perhaps? I've never used those web things, so I can not recommend what to do here, or even how it really works.
Good luck!