Multiple site with multiple databases and single login
This is not something that it easy to accomplish, your main problem will be to keep track on the users on the two instances, since users doesn't have a Global Unique ID (GUID) but instead uses the user id or uid which is a simple serial id.

You also have to figure out how to handle people editing the same profile at the same time on the two different sites, which easily can lead to some major headaches when site 1 wants to update site 2 and vice versa.

You can take a look at the bakery module which can be used for a single signup system. I'm not sure this will be useful out of the box for you, but you probably could find some inspiration to how you can handle signing in users on multiple sites.

In any regard - you will probably need some custom coding or a clever module I haven't heard off yet.