Madhyanikam need not be done after Dwadasi tiruvaradhanam and paranai.
Madhyanikam must be performed before thiruvaradhanam followed by paranai. After we do sandyavandanam, Brahmayagyam and madhyanikam must be performed before thriuvaradanam followed by paranai; there is no need to do madhyanikam again.
There will be a slight difference during Alpa Dwadasi which we will look little later.