The i inside the red circle is normal in the iPhone calendar. It is not an alert to an error. This is an information button and touching on it will show the details of a calendar. It shows the name, the people sharing the calendar, and controls such as the colour assigned to the calendar.
If you wife is sharing successfully her name will be in the list called "Shared With" on your iPhone. If not, you will see the option to Add Person. The instructions are in Share iCloud calendars on iPhone - Apple Support.
Make sure also that on the left of this display (the one generated by touching on the Calendars label at the foot of the main app screen) that your calendar(s) on your iPhone and her calendars on her iPhone have a tick in the circle. If the circle is white and not populated by a tick they will not display in the Calendar app.