when a person logs in, the login stores data for the user in session variables.
session variables are domain based, the session created on one domain cannot be used on another domain.
you could store the sessions in hidden form elements, post the form to the other domain, and use the set session value behavior to set the sessions again on the other domain, but this will become very cumbersome to manage.
what happens if the login on domain 1, post the session details to domain to, on domain 2 they update something in the account that is stored in the session? it's easy enough to rest the session on domain 2, but now you also need to account for updating it on domain 1