Transferring an iTunes library between Apple IDs, users AND computers? Okay.
So I finally got my own MacBook Pro after a few years of sharing my mother's Mac. I have my own Apple ID and everything. The thing is... I spent hours, if not Days uploading music onto her computer from legitimate sources and hard-copy CDs. I named, cataloged, sorted and optimised my playlists and I do not wish to do such a thing again, especially considering this MacBook Pro has no built in disk reader.

I understand that I can 'share' libraries with my mother's computer, but that only seems like a short term solution as I only have access to said library when I'm in close proximity to her Mac, and I see no way of simply transferring the data.

Is there a way that I can transfer an iTunes Library from one Apple ID to another over separate computers?
If it's music you ripped yourself, or is otherwise DRM-free, you can just copy the iTunes library and files over to the new computer via networked file sharing, or a USB hard drive or similar. When you open iTunes it should read the library files and load everything automatically.

Apple's support article on moving your music to a new computer should be exactly what you need.