RE: iTunes Library...
Hi,
As mwhities provides the link to Home Sharing, this should explain exactly how to accomplish what you want to do. I'll just add a couple comments.
You probably do not want to add the same music to each of the laptop's iTunes Libraries, as this would only double or triple the amount of disk space taken up by this music. Rather you want to have your Mac mini (not requiring Mac OS X Server) running a single instantiation of iTunes connected to the iTunes Library containing all of your music. You turn on Home Sharing on all of your computers (Mac mini, two laptops) using the same Apple ID. You share your entire iTunes Library on the Mac mini. Your laptops then have simultaneous access to the iTunes Library stored on the Mac mini, and each laptop can independently play different songs at the same time. The advantage of this setup is that there is only a single copy of your music and thus the minimum amount of disk storage is used for your music.
Of course, there is also the iCloud and iTunes Match that you might look into...this would also provides your laptops with your music through the iCloud.
Regards,
Switon