I think what BrandonS wants is not the position of the mouse relative to the root element, but rather the position of some descendant element.
For that, there is the TransformToAncestor method:
Point relativePoint = myVisual.TransformToAncestor(rootVisual)
.Transform(new Point(0, 0));
Where myVisual
is the element that was just double-clicked, and rootVisual
is Application.Current.MainWindow or whatever you want the position relative to.