Just wanted to add my own experience to this thread. I’ve tried many different configurations of WordPress cookie constants in wp-config without any luck. I’m setup in the same way as described by the OP using custom_user_table and meta_table.
I’ve found the session information does actually translate across different pages if you use COOKIE_DOMAIN as another answer suggested (in my case domain.com and domain.com/support) – and the session data is there but WordPress still doesn’t log you in. I’m still looking into the issue. I also found I needed to define the COOKIEHASH constant for the session data to match.
define('COOKIEHASH', md5( 'domain.com') );
You also need to make sure the salts in wp-config are identical.
Also a note to other folks that might have a similar issue – you need to set and manage user capabilities for the 2nd installation and that info is stored in the 2nd installs user meta table (even though you explicity set a different custom user meta table pointing to the primary install).