I think I do what you desire, and have for years: PC1 to manage the music library, PC2 to play the music library. (PC1 is on my desk, PC2 is in the family room.) I do this via simple file copying. The key is to have MC on both PCs set up identically.
MC is installed on both PCs. Both MCs are configured to use the same name library at the same path.
All media/music files have an identical drive letter and path on both PCs. (Identical library content locations makes the process really really easy. Using different paths on each PC adds steps and limits how cover art can be stored.)
I copy all the needed files from PC1 to PC2, specifically these:
-- All the media/music (library content) files (same path on both PCs)
-- All the cover art folder (I use a single folder for all the images and it has the same path on both PCs)
-- All the MC library files, including view layout and smartlist files (same paths on both PCs because I always explicitly set MC paths and don't let it use its defaults, though that's not strictly required for this copying technique, just be sure files are put where MC expects them)
Then (very helpful) I have MC on PC2 set to Auto Import from the folder that has all the media files. This might seem unnecessary, and maybe it is in some situations, but it gives me reliable results. When the MC files on PC2 (library and media files) are copied from PC1, thereby updating PC2, MC doesn't reliably know this happened. Running Auto Import seems necessary to trigger MC to refresh its knowledge of the library. It could be done via a manual Import, but setting MC to Auto Import means it happens whenever library content is changed.
The entire copying process is automated using Syncback SE, which runs nightly. Using a backup app is a big help. With one click it can copy all the needed files (in various folders) from PC1 to PC2 (set it and forget it). It minimizes loading each PC and the network because it only copies files to PC2 that are new/changed on PC2. (And deletes files from PC2 if no longer existing on PC1, which helps when I do some library or cover art cleanup.) And it can be scheduled as desired (mine runs middle of night) or run manually. The final benefit: I end up with a daily backup of my entire music library!
I've used this method with MC for many years because it's simple and reliable. Not counting hardware problems, I've never failed to have the MC library (and cover art and views and smartlists) I organized on PC1 ready to use on PC2. And actually, I do this process twice, from PC1 to PC2 AND from PC1 to PC3 (a laptop I use in my RV).
PS: I tried the other methods, but a simple one-way copy turned out to do exactly what I need. Of course, this limits certain features that require the various MC clients/servers to communicate, but for my music library I don't need them. For instance, I don't care how often a song is played, and I only make library changes on PC1. However, if those things matter, the syncing provided by MC must be used.