A user wouldn't be able to visit your local site at all would they? What you are talking about is a single sign-on for multiple sites. It can be done using a variety of methods by passing data in the url or through a form post.
One way to do it is to use the Server Behaviors in eCart in the "eCart->General" section. "Pass Session to Site" and "Retrieve Passed Session". It uses a form post and a back and forth verification for security to pass an entire session from one site to another. That is probably the most elegant and secure solution.