For changes on the Client to be propagated back to the Server you must have Authentication turned on in Options under Media Network, and of course allow time for the Client to synchronise back to the Server, or manually sync using the "Sync Changes with Library Server" button in the navigation tree under Playing Now>Playing from [Library name]>[Library name].
Any maintenance that involves moving files or Cover Art must be done on the Server.
To test if sync is working, make a change to a tag on the laptop. Wait a couple of minutes. Close the MC Client on the laptop. Wait a minute. Open the MC Client on the laptop.
If the tag change has disappeared, or hasn't appeared on the Server, sync between the Client and the Server isn't working, or you didn't allow enough time for the automatic sync to happen.
Try forcing a sync by;
Making a change to a tag on the laptop. Click the "Sync Changes with Library Server" button and wait for that to finish (a message is shown). Close the MC Client on the laptop. Wait a minute. Open the MC Client on the laptop.