Hi,
The problem would be that, if database is not the same, even if you can share the session token, the session data would not the same.
Joomla does not store all data in the cookie, it uses PHP session container or Mysql session container.
You problem is not an HikaShop problem or a Joomla problem (because for Joomla authentication, it would be the same problem), it's a PHP and server problem.
Sharing SSL would allow to change a part of the url/domain but would stay on the same server and the same website instance.
Regards,