I personally use Google Play Music for such purposes. But you may like to try something different. Here is an alternative service for iTunes library remote streaming.
PulpTunes is free music streaming website that lets you stream the music, stored on your computer, from any other computer device through the standard browser.
That is a common situation. You've got a huge music collection in your iTunes at home. You want to access that music from the office, at a friend's party, or let other people hear it from anywhere in the world. Install pulpTunes and make it happen - access your music from anywhere, anytime.
Note that unlike other applications, this software does not store your music on the cloud, but allows you to access the iTunes music, stored on your PC, over the Internet and control it on the other end. It is quite simple. Following the software installation, you are able to access your music from outside your home network, just pointing any browser to yoursubdomain.pulptunes.com.
* Synchronize with your iTunes and carry them anywhere
* Works with many platforms like Mac OS, Windows and Linux
* Simple to use and powerful
* Supports MP3 and AAC (M4A) files
* Displays cover art if found
* Generate direct links to songs or playlists to send to your friends
* Users/groups permission management
* Command-line mode for server environments
* Detailed logs
* Customizable footer
* Malware-free and adware-free guaranteed