If I understand the question correctly, the problem may be related to cookie domain. While browsing locally, your domain for admin and other site is same i.e localhost and that is why the session is shared.
You will need to update your web.config to specify the parent domain to share the Session. But be careful that all your cookies and session will be shared between the two sites.
<httpCookies domain=".parentDomain.com"/>
Let me know if that helps.