Is there a way to disable dragging (drag-n-drop) in a read-write dmg file?
It is not possible to disable drag-n-dropping of icons in Finder for a specific read-write DMG from within the DMG.

You should consider creating your installer in a different manner. For example consider using a read-only DMG with an app inside that the user needs to double click. When double clicked it will present a window allowing the user to drag-n-drop onto that area and doing whatever you wanted doing initially.