Relatively simple if you're good scripting with voice attack and python. I used to use my G19 to control before ED which should also work well (assuming you have a G!9 or similar of course)
Here's a good video of voice attack to control VLC:
[video=youtube;fh2C1N84w0A]https://www.youtube.com/watch?v=fh2C1N84w0A[/video]
You should be able to adapt it to tune into RS.
and the G19 App which usually has RS as one of the many stations.
http://edcodex.info/?m=tools&entry=212
As for muting Elite, don't think that's possible unless you set a macro up for it and doubt its possible to automatically do it. What I do is set VLC higher than game volume and then use VA to lower VLC volume when needed.