Observatory wasn't designed for sharing libraries between computers, but it should be possible as long as you make sure to close the library one one computer before opening it on the other one.
The errors you see on the 2nd computer are caused by the macOS sandbox security feature. By selecting the top level source folder in the Source Folders pane of the sidebar in the Observatory library, and clicking "Locate Source Folder...", then selecting it, it will give the application on the 2nd computer permission to access the images.