Since it's the iPad and iPhone, and the calendars in question are all iCloud calendars, give this a try.
Go into the iCloud settings and turn off your Calendar syncing. Tell it to delete the calendars from the local devices when it asks. This won't cause problems, because all the data is still in iCloud, not lost.
Go to the Calendar app and make sure the calendars are all gone. Restart the iPad, just to be on the safe side.
Now go back into the iCloud settings and turn your calendars back on.
Look, see what happened. Make some more tests, and see what happens.
Another thing you can try is Reset All Settings under Settings > General > Reset.
This will not delete any information or account settings. It will default many other settings, making it necessary to re-tweak things like wallpaper, sounds settings, and others. But it often clears up settings related problems that seem stuck, or unfindable.
The process looks a bit scary; because it looks a lot like you are restoring the iPad. Just make sure you don't choose Erase All Content and Settings, because that will restore the iPad and delete all your stuff.