SQL Server Cross Domain Transcational Replication Has anyone got any documentation for doing/implementing Cross Domain SQL Server 2012/2008R2/2008 transactional replication document or steps (with screenshot or without screenshot)?
Replication across non-trusted domains or workgroups can be done using Push Subscriptions in conjunction with SQL Authentication for the replication agent process accounts. Alternatively, you can also use Windows Authentication by configuring pass-through authentication.

To use pass-through authentication, create a local Windows account on both the Publisher and Subscriber that has the same username and password. Use this account for the replication agent process account and have the connections to the publisher, distributor, and/or subscriber impersonate this account. Ensure the account has the permissions required in Replication Agent Security Model.

This approach is covered in the section Use Windows Authentication to Set Up Replication Between Two Computers Running SQL Server in Non-Trusted Domains in HOW TO: Replicate Between Computers Running SQL Server in Non-Trusted Domains or Across the Internet.

If you have anymore questions, please let me know.  I hope this helps.