Configure both systems for iTunes sharing. One system is where the media and music is stored (home) and the other system is the one that is going to be used to listen to the music remotely.
Click on "edit" in the menu bar on the home system and select preferences from the drop-down menu.
Select the sharing tab and choose the option that states to share your library on your local network.
Choose whether you want to selected playlists or the entire library and decide if you want a required password to access your files.
Click on "edit" in the menu bar on the remote system and select preferences from the drop-down menu.
Select the sharing tab and click on "look for shared libraries." After this is enabled, the shared content will appear below the iTunes store in the left margin.
Install a software utility such as Simplify Media, now run by Google, or Hamachi to make your iTunes media available online. This type of software allows you to stream your shared media online and some do not require you to have your device with you. Use the installation instructions that are provided with the particular software utility that you choose and you will be streaming once the installation is complete.