NFS is what you want.
It allows a remote filesystem to appear as if it was mounted locally, so it becomes part of your directory tree. The remote filesystem is "mounted" locally, thereafter there's no "connection" to be handled - NFS handles all that invisibly for you.
IIRC there are some security considerations, but you should be fine on your LAN
You can use any tools you like to manipulate these files: the GUI, the CLI, whatever.
a link to a NFS HOWTO