The Silhouette Studio® Designer Edition provides the ability to control the hinge point for where images are rotated.
To access this feature in the Designer Edition, you may either turn on the center of rotation control point for all image that are selected (by going to the Edit > Preferences > Defaults and turning on the Center of Rotation option) or toggling the control point for each individual image (by selecting an image and pressing the letter "o" on your keyboard as a shortcut to toggle the control point on and off).
Once you have your center of rotation control point on, you will see it in the center of your image (highlighted below of emphasis):
Once your image is selected, you will see a control point located at the center of the image (highlighted in the example above for emphasis). You may click on this control point and drag it to any location.
The location of this control point (again highlighted for emphasis in the example above) will determine the new hinge for how the image is rotated.