Let see if I have understood you correctly.
You want the same session data in two domains. But you don't want to pass any information through the browser to make it possible. If that is what you want then it is impossible. You can't both keep the cake and eat it. Sessions are linked to the domain, so it is not possible to do this. You can't do it with cookies either.
Just one question before I start with a suggestion: Do you use an encrypted connection when logging in, like https? If you don't then it won't be much worse to allow this since it is easy to listening to the traffic anyway.
But what about this way, you save the session in a database in the admin. You also store a username, a random value and the time it was created. The random value changes every time you load a page, so does of course the time. Then you can call the new page with "www.newpage.com/page.php?un=$username&random=$randvalue". When someone uses those variables you check it against the database, and if the username and random value matches they get access to the session data. With the time you can set that they have to use that link in x seconds after the last page load.
Note that this suggestion is not safe, it would be very easy for someone listening to the traffic to use that information. Because of that it should never be possible to go from the webpage to the admin panel, only the other way. You can of course store more information in the database (IP as an example), but it won't make it bulletproof.
