How to stop synch of Desktops?

Just upgraded to 10.13.2 on iMac and my wife's Macbook pro. After restart my wife logged in as an unprivileged user and did something that caused iCloud to merge the desktops on the two machines. It removed all the content from her desktop and put them on iCloud and put the contents of my desktop on hers. Now it is putting the contents of her desktop on mine. Trying to delete an unwanted file from one or the other gets a bunch of warning messages about data being deleted from iCloud. Trying to remove desktop from iCloud options also gets warning message.

How do I get merging to stop without losing any data? We would like to have each desktop separate on each machine but still mirrored separately on iCloud, and other applications, like calendar and notifications, synched, but not the files on the desktop.

Both machines have the same account names for admin and unprivileged user, and both are managed under the same Apple ID. Is that part of the problem?