Relation: add button to create node related to current node
The Node Reference URL module works with the References module to accomplish this feature. When you add a node reference field, you can specify Reference From URL widget which will auto fill the field from a value in the URL. You can also specify (in the field settings) to display a link on the referenceable node.

In your case, you would create a node reference field on School News that references Shools. Just select the Reference From URL widget and configure as necessary.

There's an older lullabot video about creating image galleries in Drupal 6 that demonstrates how it works. The Drupal 7 version has the same features and works the same way.