Google two-factor doesn't work on iPad after iPhone is set up

I have this set up on my iPad and iPhone. Google's site isn't very clear, and it's easy to get confused between the different elements of the two factor logins.

It sounds like what you're getting hung up on is the Google authenticator app. That's only used for logging in to Google's websites, it doesn't authenticate your iPhone/iPad for email access or anything else. For mail access, all you need (and the only thing that will work) are app specific passwords.

Here's what I did:

1. Go to this page and generate an app-specific password. Label it iPhone Mail. (Doing this on the actual device is probably best, since you can copy/paste rather than manually copying from your Mac).
2. Open your iPhone Mail settings, and input the password you generated into your Gmail account settings.
3. Repeat for the iPad (creating a different app-specific password is highly recommended).

That should be all you need.

I think the reason you had trouble with the authenticator on your iPad is that Google probably allows only one authenticator active at a time for security purposes. I'm not 100% sure on this, but it's my best guess. I'd suggest keeping it on whatever device you have with you more often (guessing that's your iPhone).