I have a similar setup. There are two ways to go about this:
1. First, use syncthing to keep the actual files in sync between the two computers.
2a. If the file paths on both systems are exactly the same, you can choose one computer to have the master library, and use MC's Library Server on the second machine with the option to play a local version of the file if found, checked. This will keep everything in sync and keep network traffic to a minimum. If you really need to use the master library on the secondary client machine (say you are traveling without internet access), then you can also use syncthing to sync the master library's automatic library backup directory. Then you can just restore the master library on the client.
2b. If the file paths are different (this is my issue, since I use MC on Windows and Linux) OR you wish to have a truly independent MC library on both machines, then make sure that MC is set to automatically update the file tags when the library changes. Then, if you retag the file, or add a rating, etc, the new file tags will be written to the actual file, causing syncthing to sync the file with the new tags. The only problem with this approach currently, is that there is no simple way to handle syncing the playlists.