In reply to john arran:
Just mirroring the phone's screen does work for almost any app but it's a much clunkier and less elegant solution and as far as I'm aware it's not yet available on all android devices. It's also rather dependent on the quality of the network you're connected to. A fast, modern WiFi network that both phone and Chromecast have a good connection to might give decent results. An older router or poor signal quality would give decidedly worse results for screen mirroring than proper casting supported by the app.
In essence, Sky have no interest in making it any easier for you to use your Sky subscription on any TV other than your own. They're happy to let you watch it on your mobile because they don't think that will damage their sales but they'd much prefer your Dad to be forced into buying a separate subscription.
You could try the screen mirroring idea, it might work well for you if your phone supports it and your Dad's network is up to the task. Alternatively, as another long shot, you could look into whether your phone or tablet itself supports video output to the TV. Various options are described here:
http://www.pcadvisor.co.uk/how-to/google-android/how-connect-android-tv-353...