Why doesn’t iTunes allow me to reset the Music library

Yes it is, if you've set up the iTunes libraries for home sharing. Turn on iTunes on the machine with all the music. Go to iTunes on the machine you want the music on, then open look for other iTunes libraries on the network. If you don't see share libraries you may need to update the menu options in the General settings. Browse to the songs you want highlight them then click import in the bottom of the iTunes window.

I use this all the time to move songs, movies, TV Shows between my main desktop with a few TB's of storage and the different laptops around the house. This also works between OS X and Windows environments since it's connecting with iTunes.

EDIT: You can also configure the main iTunes library to automatically sync songs from the other libraries. This would mean that you only need to hook up a monitor once to set up the share the first time. You could also use this time to set up a VNC client on the main machine from which you could access the computer with your laptops and make edits as needed.

You need to make sure your iPhone is configured to sync music from iTunes:

• Connect your iPhone to your computer
• Start iTunes
• Select you iPhone in Devices list
• Select Music tab
• Check the box Sync Music and select what you want to sync to your iPhone (all music / specific playlists)

Also make sure to "Sync only checked songs and videos" option is not checked on your iPhone Summary tab.

On your next sync (automatic or manual, depending on your settings) music should begin to sync to your iPhone.