Ok first point about your current mobile version, when you click on a channel the popup window is too cluttered, I have just clicked on BoxUK and i'm presented with an "auto starting" stream, sorry don't like that! In my view it's upto the person to click play to start the stream, after all I might not want to listen to the stream right then I might be after your rota and a stream that auto starts will annoy me! Not saying i'm right on this, just my thoughts. In total on that page I have three players and a chat box, needs cleaning up,
less it more 
One site and address should do it all, not multiple ones, once again just my thoughts, but I can see what you've done and can maybe see why you have it setup the way it is at present.
The Wordpress theme you have is miles better and cannot be compared. I have tried it on my phone and it displays ok and does appear to be responsive
However, just be aware of the size of your images etc as you'll find with a responsive template they can ruin it if they are too wide and you'll get a left to right scroll bar (personal bug bare).
Plan your homepage and other pages so you don't need to redesign them all again a few months time. Remember your visitor shouldn't be anymore than 3 clicks away from the content they want where possible. Think about what
you do when visiting a website, people will NOT LOOK for something, it HAS TO BE EASY to navigate a site or they'll just click off your site and probably not return again. Look at other professional legal stations, BBC etc and see what they do, not saying copy them, but look at how you access content or streams etc etc Design your site, or access to your content in a similar way, after all their sites work as they cost thousands!
For more info on your Wordpress theme and it's functions refer to it's documentation
