I use a laptop with external USB drive with excellent results. In fact, I listen to it while bouncing down the road in a car or motor home.
My method, slightly simplified, is this:
My MC library on my desktop is on a second drive, letter M: (MC itself is installed per default on drive C).
On the laptop with MC I assign the external USB drive letter M: (via Windows > My Computer > Manage, or other utilities).
I store my library (which includes playlists), music files, cover art, saved views, visualizations, and everything else that is configurable in MC on M: (actually, M:\data\, my preference).
Note: I feel it is better to not use MC's "Default" library. My library is called "music".
Both computers use exactly the same M: paths, so there's no need to modify the library. I just copy all the files from desktop to laptop. (Of course, if having identical drive letters is not possible, the step of editing the path is necessary as explained by Alex B.)
To do the copying I use a backup program (SyncBackSE, but just about any should work) because it's fast, smart about only copying files that have changed, and because I can set up all the folders I desire to copy and do it with one click.
Periodically I connect the USB drive to the desktop and run the backup process. (Of course, the USB drive gets another letter when on the desktop because M already exists, but that doesn't affect the "M:" letter it is assigned on the laptop.)
I've been doing this method for several years (been using MC/MJ since version 7) -- it's simple and reliable. Because I'm copying my entire MC "data" set, it doesn't matter that I add or delete or change music or cover art or views or whatever. It all gets handled by the backup process. The only "challenge" arises when MC moves to a new version (14 to 15, for instance); then I check and possibly do a little tweaking of MC config and the backup setup.
There are other methods built into MC, such as using MC to synchronize to the USB drive as a device, or using MC client on the laptop to synchronize with MC server on the desktop, but for my situation these are more complex, not as versatile, and slower to do the job. But in other situations they are the best methods.