Ok over the weekend I set up a test iCloud calendar on my phone and went through the same share options you have done and shared with another iCloud user.
They received an email from
noreply@insideicloud.icloud.com which contained the invitation. Click on the Join Calendar link on their iPhone added the shared calendar and it was visible from myCal PRO. We can then both add and edit events and they appear on each others device within a minute or so (when connected over wifi).
I would suggest removing your wife from the shared list in that calendar and trying again. Best to make sure you share with your wife's iCloud account email address.
Let me know how you get on!
Regards
John