I searched and researched. What I came up with was a couple of apps from Playa Apps - Contacts Sync for Google Gmail with Auto Sync and A2Z Contacts. They both have really good ratings and reviews and only cost 99¢ each.
I'm using the Google Gmail app on my iPad and have the contacts syncing with CardDAV. It all works perfectly. No thanks to Google for killing the Exchange ActiveSync interface. It wasn't obvious what I had to do to that configuration to coexist with Contacts Sync so I wrote an e-mail to Playa App's support.
Being anxious I just popped for the 99¢ and installed the app. It prompted me to read the user guide inside the app which explained to turn off CardDAV. That worked fine and the contacts synced perfectly
Then I tried to send an e-mail to one of those groups using the Gmail iOS app and couldn't find how to do that. I then came across "A2Z Contacts - Contact Manager." Again it wasn't obvious if it would let me send e-mail to groups using the Gmail iOS app or did it have its own mail interface?
99¢ later I had the installed A2Z Contacts and the user guide inside the app explained it allows you to send group emails from it's own interface and it also allows you to create "email lists" to send group emails directly from the Mail app or the Gmail app.
So off I went to exercise it.
First, on the iTunes page for "Contacts Sync for Google Gmail with Auto Sync" it says "SYNCS AUTOMATICALLY!"
Nope. Not so much.
When you try to set it to sync automatically you get this:
Maybe I should have known this but the iTunes section on In-App purchases wasn't clear.
The user guide cautions to ensure that there aren't duplicate contacts in Google Contacts so I checked that.
But "Contacts Sync" thinks differently.
And the referenced log didn't help me resolve this.
But I proceeded and tried to use A2Z to create an "e-mail list" the process worked fine. Until I got this screen:
"Periodically update your e-mail lists in A2Z Contacts so that they match the latest data in your groups."
I'm trying to do this so my wife can send e-mails to a group that she maintains in web Gmail. There are just too many manual steps in this process.
I don't fault the developer of these apps at all. He has been prompt and helpful in his responses. I realize the limitations that Apple puts on developers.
The only alternative I see is for me to manually create the same type of "e-mail list" on the web Gmail and let her use it from her iPhone Gmail app.