I have done exactly what you described. I have two machines that have the same music library, local to each machine. So I don't have to have one running and share the music to enjoy the music.
The way it works is rather simple. Copy the entire iTunes Music directory from one machine to the other. In my case it was from the Apple to the Windows (yuck) computer. Then run iTunes in Windows and tell it where the directory is that has the music. It should ask you to Authorize the computer (if it hasn't been already). Once it is authorized, then you are good to go.
A note to anyone that might think that this is pirating the music, it isn't. You are still required to Authorize the computer. By Apple music license, this is one way that it works.
I hope this works for you! Enjoy!
Take Care,
Quark