First, when you are using Virtuemart, you have to check its configuration to ensure that "secure site" URL is the correct one and that you are not redirected to another website.
If you are connected on the correct website and that you want to share the user login between the website and also benefit of the single sign-in, this is possible when you share the users and that you have the website on the same domain. The websites can be a subdomain or a subdirectory of a same domain.
To see how to create websites that share the users, see the video 16
www.jms2win.com/en/tutorial#jms12x-16