My company has a setup as follows:
Include a script tag from domain2 that sets the cookie using a username and hashed password:
You can then check to ensure that the hashed passwords match (one way).
Key points:
Make the hashes in the URL time sensitive by appending a timestamp that will be agreed upon by the server (for example, 16:00, 16:10, etc) before hashing the string. If you're using HTTPS this is less of an issue.
If your passwords are already hashed, it wont hurt to double-hash the passwords assuming the salts are the same on both servers.
Sample PHP code:
src:
dest: