There's a way to do it, but not as you are doing it. First, you need to stop thinking about your sky dish as similar to your aerial - it's not. Your tv aerial receives all frequencies of analogue broadcast on UHF (and VHF too in Ireland). It then sends these to your tv which accepts certain frequencies as points that it can be set to, hence your tv has different channels.
BUT - your sky dish receives digital frequencies. Your sky box tells it which specific frequency to choose, and the LNB - the little arm doohickey - handles it so that only one frequency comes to your tv at a time. Following so far?
Now, you can have more than one LNB output from your dish. This allows two or four frequencies down to separate boxes which decode into separate tvs.
So what can you do? You can either have a multi LNB installed - double or quad - and link to your 2nd box, or you can go to argos and get a link cable which allows a 2nd tv connect to your system (but you can only still watch the same channel that the other tv is watching.)