Basically does your TV have enough video inputs (HDMI, Scart, SVHS, Component, Composite or UHF Aerial) to be able to plug in all your components (Sky, DVD, PS3, VCR etc) directly?
This would allow you to use the TV remote to choose what to watch (probably like you do at present). The audio signals from these components can then be fed to a stereo amp and use that to select what to listen to.
Switching picture and audio seperately through the TV and amp is a little less elegant than switching both with 1 button on an AV amp perhaps but is no big problem.