Resize content in a dockpanel

What do you mean by resize? A dockpanel would do some amount of resizing the children to fit -- based on the settings of individual elements (like are they set to Auto heights and widths or specific H & Ws). If the property LastChildFill is set, then the last element to be added as a child is automatically stretched to fill the remaining space.

If you want to scale a UI, you might look at a ViewBox.

someObject.SetValue(someObjectClass.WidthProperty, "Auto"); should work

The reason you can't use someWPFObject.Width is because I believe it is actually the value converter that handles the special case of Auto.

in code:
vc_clone.SetValue(DockPanel.HeightProperty, Double.NaN)