Welcome to the Techreport Forums!
I'll take the first crack.
I need to know two things though:
1. What motherboard is in your system
2. What operating system are you using
In Windows 7, it is trivial to assign programs to different audio devices, be they the HDMI output on a video card, the digital output on a soundcard, etc. I'm currently using the onboard Realtek as a digital 2.1 output to a surround sound receiver for my system, but I can easily switch this to analog for a headset as well as to the monitor's speakers (which I don't, as they're awful).
It also seems that you're trying to use a computer both as a workstation and as an HTPC concurrently. I don't think that this is a bad idea, but understand that it's going to require more management on your end for everything you do; everytime you switch from one function to the other you'll have to change settings, but this is very doable.
To switch between sound on the PC and digital out for a show, try using just one application for show viewing, and assign its audio output to the digital output only. If your board has a digital audio out I'd suggest using it for this purpose; it should also be able to pass encoded surround sound tracks directly to the receiver if the files have them.
With your video card outputting only video over the digital link, I'd suggest not hooking it up to the receiver at all, and just using the digital output on your motherboard as above. Otherwise the receiver may be confused as to what it's supposed to be looking for, but you shouldn't otherwise experience a problem. The main issue will be with HDCP and audio- if you intend to play Blu-rays or other HDCP encoded content, this solution will not work; you'll probably want to upgrade to a video card that can handle audio over HDMI as well.
Canon 6D||[24-105/4L IS USM|100/2.8L Macro IS USM|70-300/4-5.6 IS USM|40/2.8 STM|50/1.4 USM|85/1.8 USM|Samyang/Bower 14/2.8 Full-Manual Rectilinear Wide-angle|
Canon EOS-M|11-22/4-5.6 IS STM|22/2 STM|EF-M 18-55/3.5-5.6 IS STM|
For sale!|24/2.8 IS USM|