Is it possible to create two OSSN websites and link them together so that the user can navigate from one site to another without forcing themselves to reconnect?
There is no ready solution your developer need to figure out this and make the logic design.
They may use API https://www.opensource-socialnetwork.org/webservices/view/3570/user-authenticate
Or writing own API to auto login
How would you do that! I mean ! We are talking about php or database programming