[AFreeBird]

Logitech Touch Mouse for your iDevice. Works just like you described except the keyboard is virtual when needed, which is not all that often.

[ReignOfError]

Mobile Mouse is the app I use with my Mac Mini home theater box. It's great at the trackpad function, and the keyboards are customizable for each application on the Mac -- movie controllers for Quicktime, back and next buttons for Safari, etc.

It's also supported on Windows, but I don't have first-hand experience with it.