Answers-
1/ Only emails sent from the MacBook Pro are affected. Before I signed out & back in to iCloud I could see the sent emails from my @icloud.com account from the MacBook Pro on that device but I could not see @icloud.com messages sent from any other device. On all other devices I could see all of those but not the ones sent from the Mac/pro.
Since signing back in to iCloud I can see messages sent from the @icloud.com account on the Mac/pro since then on it & all other devices but I cannot see any of the @icloud.com messages sent from the Mac/pro before the sign out/in on any device.
2/ I only use Mail on all Apple devices.
3/ Since signing out & in I can send & receive messages on both the @me.com & the @icloud.com accounts without any issues, whichever device I use.
Trying to think back to the time this issue must have arisen, I think it must have been when The Management got her first iPad in about April 2015 because she was never able to see those messages. I never did anything about it then because it was quite convenient that she couldn't read them but when I couldn't read my own messages if I was in the wrong place, I thought that was going too far.
I can find the Mail backup files in Finder & I can look at them but although some bits are in plain text, the majority looks like the output from an Enigma machine, which wouldn't help me look back to see if I had insulted someone in the past, or if I
needed to do so now.
Many thanks for your help so far & I do hope you don't get bored with this subject before I get it sorted.