While the Remote app provides only control of a computer or Apple TV, there is a feature of iTunes called Home Sharing that would provide for the ability to play your content on your iOS device.
Home Sharing in iTunes is designed to let you easily share your iTunes media libraries between up to five computers in your household. You can also use Home Sharing to play your iTunes content on your iOS devices and Apple TV (2nd generation) if they are connected to your home Wi-Fi network.
Home Sharing your iTunes library with your iPhone, iPad, iPod touch and Apple TV (2nd generation)
Home Sharing can also extend streaming of music, movies, TV shows, and more to your iOS devices and Apple TV (2nd generation). To stream music, movies, TV shows, and more to the multiple iPhone, iPad, and iPod touch devices in your family, as well as your Apple TV (2nd generation), you will need to turn on Home Sharing on the devices. You'll also need to use the same Apple ID on each device on your home Wi-Fi network.
Note: iOS 4.3 or later is required for Home Sharing on iOS, and Apple TV (2nd generation)or later for Apple TV.
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