So, two databases, but only one users table?
Provided both sites can log onto the DB with the users table, that would work just fine (though probably not how you expect - users would still sign in twice. If the sites need to share data, pull from only one DB. If it's a load issue, use load balancing over two (or more) servers. You'd need to talk to your host or hire dedicated it guy for something like this).
I would go about it differently - use AJAX to send the user's login cookie when you're not on the same domain. Store the cookie value -along with the session info- in your DB so you can check it from either site.
sorry, to clarify -- you would need to add a hidden iframe (or something) that points to the first domain, in order to make the cookie available.
you might also use html5 cross-document messaging, where it's supported. I don't have first-hand experience with either of these methods, unfortunately, but it should be fairly easy to find resources for.
Edit:
on second thought, this is now my recommendation:
for your users that allow third-party cookies, you could simply set a "logged in" cookie for both domains when the user signs in to one or the other.
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