No you should not configure second domain as separate site, instead use it as alias for primary domain like you did in Step 1. If domain2 redirects to domain1, it means your DNS/vHost configuration is good… your internal Wordpress internal routing is NOT working.
You have not mentioned what you did inside it so better paste a screenshot to see if it is correctly setup.
WPML should have option to setup multi-domain. Ref :https://cdn.wpml.org/wp-content/uploads/2021/04/typing-in-german-domain-name-wpml-1.png
