Running Redis as an external cache server for Redmine
Redmine doesn't store any session data in its cache. Thus, configuring your two Redmines to use the same cache won't help.
By default Redmine stores the user sessions in a signed cookie sent to the user's browser without any server-local session storage. Since the session cookie is signed with a private key, you need to make sure that all installations using the same sessions also use the same application secret (and code and database).
Depending on how you have setup your Redmine, this secret is typically either stored in config/initializers/secret_token.rb or config/secrets.yml (relative to your Redmine installation directory). Make sure that you use the same secret here on both your Redmines.