I am not so sure you can get them on the domain remotely. I have a question. Why are you remoting in and trying to access the database that is mapped on a client? Why not just remote to the server directly?
I'm sorry. I think I keep missing a small detail each time.
Also, when you say "see" the database files. Do you mean, the laptops see the desktop remotely and then, of course, can see the database which is mapped? That would make sense. Of course, then you could run AC from the host desktop. You would also be able to browse to any file that you could browse to if you were on the domain. But, you would not be able to open AC on your laptop, reset the path and then try to browse directly to a database on the server. Even if you could, the Internet speed would not be nearly fast enough to use the database.