Thank you again for your reply.
Okay. Sure enough, the Reminders data is there. However, I seem to have several potential conflicts now. (Note: this is not a comprehensive list.) At first sight, the calendar data appears to be slightly different and some items are no longer showing. Also, I am concerned that whatever I do using the 'other account' will affect my Time Machine backups. I have therefore logged out and logged back in to the other account (I hope this makes sense).
My 'non-qualified' view is that I have inadvertently created a two users and my data has been split across these users, e.g. the Reminders info. In my simple terms, it looks like I need to merge these two 'users' such that I end up with only one, where all of our data resides. Sounds simple, but I assume this isn't. Any thoughts.