Is there a way for a user to change their password on multiple databases (external) that are related all at one time?
You can use scripting to accomplish this. The script would prompt for the password and then run scripts in each of the other databases that update the user's password to that password.
If you have a number of databases, have you considered using external authentication through Active Directory or Open Directory or even OAuth?
If external authentication or oAuth isn't an option, here's a module that might get you started:
Retrieving data ...