If you have two different blogs running, you'll need to make sure the code you're including knows which database to access, otherwise it will simply access the database of the blog doing the including, instead of the blog it started in.
There are a few ways to do this, the way I would probably do it is to change the widget to output some html and file_get_contents that.
So for example
// blog's news-widget.php
// pull some info from the database
// output html directly
// main site
Not very hard, you just need to approach it slightly differently than you are now