It's possible to do both things. With the second one, a "sort of shared library" is exactly what you'll get, "sort of" being the key words.

Moving the library folder is the easy part and getting multiple copies of iTunes to reference that library can be a mixed bag. I've had it work in the past with two Macs, but I no longer do it because I was using both a Mac and Windows system which didn't work out too well. I'm sure two Windows systems would likely work as well as the two Macs did though. Some people say it works well with one of each.

I don't know if you keep your music files within your iTunes library folder, but if you move your music files, you'll probably have to drag them back into iTunes to have it refresh their locations. This *might* be taken care of automatically if they're within the library folder hierarchy.

Anyway, start by copying the library folder to the new location, but don't delete the original. iTunes shouldn't be running at the time. If your music is within this folder structure you can then move to opening iTunes (read below). Otherwise you can now also copy your music to its new location.

Next you will open iTunes but you'll hold down a key to pop up a prompt to allow you to choose a different library. On the Mac, you should hold down the OPTION key as it's opening. For Windows you'll hold down SHIFT.

You'll see a prompt that allows you to create a new library or pick the location of an alternate library to use. Find the copy you made above and it should load in as before.

If your music was within the library hierarchy, hopefully iTunes will update its location and you should be able to play any track you click on. If not, and you've moved your music as well, then you may notice that when you try to play a track a small "!" appears next to it telling you iTunes doesn't know where the music is.

You have two options here. Drag all the music back into iTunes and hope it updates everything, or first delete all music from iTunes and then drag it all in. The second method will definitely avoid duplicates.

On the second computer, just launch iTunes with the key down as above and point it to the new library - once the library has been all sorted out with regards to music location of course.

GIve it a shot.