Have to login twice for i18n multisite using "Domain name only" language switching

I have set up a multisite and am using domain-name switching between English and French. However, I want to have a shared, automatic, login between the two languages.

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Let's call the domains:
http://apple.org
http://pomme.org

I am sharing users between the sites, and a user can log in to apple.org with the same username and password they use on pomme.org. However, when they switch languages, they have to re-login to the site. What I want is for that login to persist across the domains. When they are on apple.org and click the Francais link, I want them to be able to already be logged in on pomme.org.

This is also a problem (not do with i18n in this other case) because I want to be able to share the login -- not only across apple.org and pomme.org -- but also with other domains in the multisite (e.g., banana.org). Those sites also share users, but they have their own database prefixes.
Again, I can share user and login information across the sites, but I want the login to persist between the domains. When I tried setting singlesignon up on apple.org (as the controller) and banana.org (as the client), whenever I try to go anywhere on banana.org, I get redirected to the following http://apple.orghttp%2F%2Fbanana.org%2Fsinglesignon%2Fassociate%3Forigin... 3A &rn=yVW0IwipVG27Ubx&rg=.

I'm not sure what I'm doing wrong here, or if singlesignon is able to create persistent and automatic logins across multiple domains on an i18n multisite. Any help would be greatly appreciated.

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I have tried using the Single Sign On (sso) module, as well as a couple of other modules (e.g., Fierce SSO and the old Shared Sign On module), but without success.

One problem with Single Sign On, in this context, seems to be that -- in terms of i18n -- the domains aren't actually using different databases. The only difference between them is their settings.php file. So in the case of different domains, we don't have a separate client and controller. "Only one single sign-on module can be installed at a time. Please disable single sign-on client or controller on this site."

We had tried using painless sign on (http://drupal.org/node/181176) earlier as well, and that worked on the multisite originally (when I would go to http::multisite.org/apple or http://multisite.org/banana), until we started using separate domains.

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Both of the sites are running from a single multisite. Let's call it:

http://multisite.org

So they are set up using the following directories in Drupal:

/sites/apple.org
/sites/pomme.org

In the settings.php files, I have this set up for both the apple.org and pomme.org domains:
$db_prefix = array(
'default' => 'apple_',
'users' => 'shared_',
'sessions' => 'shared_',

);

For the banana.org domain, it is slightly different:
$db_prefix = array(
'default' => 'banana_',
'users' => 'shared_',
'sessions' => 'shared_',

);