I have been successfully able to run a Custom Login Page for Google Apps until today. I used to use Client for the Google Apps Provisioning service. using which we could send email (username) and password as parameters and obtain the authentication token.
With OAuth2 (as per Google we need to upgrade to OAuth2 starting 20th April, 2015) I can't find a solution! There's no way I can send/ check if a username/ password pair is correct.
There is no way now to do what you want. You could use SAML2 and then use Google as the source IDP via OpenID but you would end seeing the Google Login page again. It seems that you are trying to hide the fact that it is a Google shop.
SAML2 auth lets you design your own login screen but requires that you use your own user database.