1 WordPress, 2 themes, 2 domains, 2 servers

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I can think of 2 approaches to try:

  1. You can use a referrer variable within the link such as:
    domain-two.net/blog/?ref=blog2

The receiving blog should watch out for the content of the ref variable.

  1. You can just copy domain-one.com into domain-two.net/blog, then access the database of domain-one.com remotely via wp-config.php