Thank you for your message.
I took a look at your site and it appears that you have a lot of customization on your login page at /wp-login.php. I imagine some of this custom coding, or other plugins, are preventing the Google Apps Login plugin from doing its work.
If you are able to remove some of the other plugins, we might be able to get it to work.
However, looking at the other login types you have already, my guess is that those ‘social login’ plugins (allowing new users to register for accounts via Facebook, Google etc) will be better for your site.
Google Apps Login is better where you have a fixed set of users (e.g. only employees within your company) who need to login quickly and securely.
I hope this helps – good luck with your site!
Dan