This is called "interlacing". Or, more specifically, it is what happens when you resize "interlaced" material
without deinterlacing it first.
Applying a deinterlacing filter is the right thing to do. But you have to be absolutely sure that you apply the deinterlacing filter on the
original "interlaced" material -
prior to any resizing.
Once "interlaced" material has been resized
without deinterlacing it first, it is pretty much impossible to fix/undo, except by going back to the original unprocessed footage.
If you expect more help, please upload a small(!) and completely unprocessed(!) chunk from your original DVD...
See also: http://100fps.com/