Is there a module that will pass the authentication request off to a second Drupal site, ideally to an out-of-the-box services endpoint?
There are some similar questions about login integration with other systems, but I couldn't find a Drupal-to-Drupal question.
Have you checked out the Multisite Login module? This allows sharing logins across different domains, and I've had luck with it. They also have a Drupal 7 version available in dev.
Another option might be to set up whichever site you want to be responsible for authentication as an OpenID provider then on the other site enable OpenID (core module) for users to log in. You can set up the first site as an OpenID provider; I've never done this, but it should work in theory.
There are some option to achieve this job
1. Single Sign On Multiple Domain
Single Sign On Multiple Domain module allows login to multiple drupal websites from a single website. If you have multiple drupal website installed at either on same server or other server, then you just need to login to one and it will login you to other websites as configured in the configuration page. For this you have to install this module in all website and do required settings.
This module also allows to create account for user if user do not exist in other website. It also allows you to synchronize user role while creating account.
Multisite Login allows a user to login to all sites in a multisite configuration, even though the multisites do not share domain names.
For example: politicker.com politickernj.com politickerny.com
etc.NOTE: if you are using several sites on the same domain (ex. politicker.com, nj.politicker.com, ny.politicker.com, etc.), then you do not need this module. The multisite functionality in Drupal core has the ability to share logins for sites like these without additional modules.
This module was designed to be an alternative to the singlesignon module but using a technique that does not block search engines from accessing your websites.
This module implements an OpenID Provider in Drupal based on the OpenID Authentication 2.0 specification. It turns your Drupal site into an OpenID provider and allows users of your site to login to any other OpenID-enabled site using their Drupal password and identity.
According of my experiences I suggest first try Single Sign On Multiple Domain module
