Calendar delegation issue

According to this article : Calendar (El Capitan): Add or delete calendars

Delete a calendar

1. Click the calendar’s name in the calendar list.If you don’t see the calendar list on the left, choose View > Show Calendar List.
2. Choose Edit > Delete.Some calendars can’t be deleted.
   • You can’t delete delegated calendars, but you can stop showing them in the main Calendar window. For more information, see Share calendar accounts.
   • If you can’t delete a calendar for a particular calendar account, try deleting the calendar on the account provider’s website. For example, to delete a Google calendar, go to google.com.
   • If a calendar account has only one calendar (not counting other people’s calendars you’re sharing), you can’t delete that last calendar.

You are showing an iCloud CALDAV (the calendar protocol) account on the picture you posted as well. That iCloud calendar will also be superimposed in the main Calendar view unless it is disabled. If you have the colleague's calendar shared there as well, It could be the source of the multiple instances.

You are currently viewing the combined information from BOTH Calendars -- one on iCloud and one on InteliHub.

Which do you want to be the ONE Master calendar?

Once you decide, look at the Account you will NOT be using going forward. Click the pane in the header showing "Account Information" and uncheck:

[√] Enable this Account

The screen shot you posted shows Kate's account as a delegate. It shows three more that do not have titles.

Are you certain these are Kate's accounts? Could they be other calendars on your dad's account or from somewhere else?

If they are Kate's account, does she have multiple calendars intertwined and pointing back to themselves like this? Does she show multiple calendars when she looks at this?

One possible fix is to write down all the information for all the accounts, delete the accounts and add them back in, in hopes of fixing the Accounts database. The individual appointments should stay, it is only the Sharing mechanism you are re-building.