For your laptop turn on Home Sharing Making a note of what Apple ID you use.
Do the same for your other computer using the SAME apple ID it does not matter if it uses a different ID in the itunes store
If you cannot see the Home Sharing Icon
Ctrl + S to show the sidebar and the other computer library should be displayed under Shared
View > Show Sidebar for a Mac
Select the other computer library. select what you wish to copy over and click import at the bottom right