how do I move music to another computer only network?

I will provide one answer but your question needs more detail before deciding if it is the best answer.

Share your iTunes library over your home network - Apple Support - https://support.apple.com/en-us/HT201779 - about Music Sharing and Home Sharing

Home Sharing Support page - http://www.apple.com/support/homesharing/

iTunes 12 for Mac: Use Home Sharing to import items from another iTunes library - https://support.apple.com/kb/PH19614

iTunes: Setting up Home Sharing on your computer - http://support.apple.com/kb/HT4620

Understanding Home Sharing - http://support.apple.com/kb/HT3819