I have a very similar issue that seems to have started about 4 days ago. I first noticed it when the color of my wife's shared calendar (our family calendar) changed, and I couldn't change it back. It was very annoying, because the color changed to blue, and my personal calendar was already blue. I couldn't tell them apart.
When I would try to change the color of her calendar, it would appear changed, but would change back automatically or if refreshed. In an attempt to solve it, I removed her calendar and asked her to re-invite me.
Here's where it gets very odd.
Now, if she invites ME to view the calendar, I will get an email notification. However, my FATHER will get the notification in his calendar app (or in the iCloud.com app).
This is very easy to reproduce. I opened 3 different browsers: Firefox, Opera, and Safari.
In Safari, I logged into iCloud.com as my dad.
In Opera, I logged into iCloud.com as my wife.
In Firefox, I logged into iCloud.com as me.
In my wife's iCloud.com calendar, if I add my email address as someone to share the calendar with, I will get an email. The notification will show up on my dad's iCloud.com account in Safari.
In my dad's iCloud.com calendar, if I add my email address as someone to share the "Work" calendar with, I get an error that says...
Couldn't share "Work".
Your changes to this calendar couldn't be saved because of a server error. Please try again.
I've been trying for several days now.
How can I fix this problem? I feel like there is something really screwed up with my iCloud.com account!