iCloud features requiring use of @icloud.com account versus actual account name My wife and I use several features of iCloud, like calendars, reminders, and more. We are also using the new Family Sharing features of iOS 8, but this issue existed before then, and still happens today. 

For some reason, if I want to connect anything between our accounts, I must use her @icloud.com account associated with her account, not her general gmail account. This gets to be annoying, because we never remember, and she doesn't use that @icloud.com account for anything. 

She can sign into iCloud on her devices and the web with her gmail account. 

If I share to her gmail account, it never gets to her. If I share to her @icloud.com account, she gets all invites, and actually gets the notifications in her Gmail. 

How do I get this to work without the extra account?
I had a similar issue and eventually got sick of dealing with the issues you have noticed and gave in and used the icloud account. Calendar, app store, reminders, notes, etc. It all works better with the icloud account. I never use the email address associated with it (and I've had one since the @me.com days).

Yes it is annoying but Apple's built-in apps work much better with Apple's accounts. You can spend hours of your time troubleshooting or moving over to dedicated 3rd party apps or just "grin and bear it."

I know that doesn't solve your problem, per se. And there may be folks who have found acceptable workarounds (if not here try macintouch.com) who can offer a better solution but I found that not fighting city hall ended up working for me rather well after all... YMMV...