This screen shot shows the Maven POM (Bulk) Updater app. Above the TableView, there are 3 Buttons. Two (select and de-select) are aligned to the left. The third, lock, is aligned to the right.
|A Toolbar with Buttons Aligned both Left and Right|
Here is the hierarchy and settings for the rightmost HBox.
|Rightmost HBox has Alignment Set to TOP_RIGHT|
In my opening paragraph, I suggested "when in doubt, wrap". I was trying to get the right Button to stick to the right by manipulating the enclosing GridPane and the Button itself. However, when I simply wrapped the Button in an HBox (as with the left buttons), and flipped a setting my layout worked.