How to log user in to multiple drupal sites?
You are looking for Multisite Login module

Multisite Login allows a user to login to all sites in a multisite
configuration, even though the multisites do not share domain names.
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.

also take a look at CAS module.