Unless I am misunderstanding something, a published data source from one Tableau Server or Tableau Online site cannot be published to another Tableau Server or Tableau Online site. A local copy of the data source would need to be created then published to the new server or site. Another option is publishing the data source directly to the new site or Tableau Server with the credentials(Server name/ ip and password depending on the data source) to the data source and not the Tableau Server data source.
Additional information and options for dealing with multiple Tableau Server instances.
Hope this helps!