I also had tears at the birth of the baby Jesus in The Nativity Story. It was a stunning, exhilarating moment.
I would have preferred the actual birth of Jesus remain a miracle and a mystery. Although I very much enjoyed the movie and would recommend it to any adult,I would never take my grandchildren to it.
They are all under ten and I have no interest in spending any time discussing childbirth with them,neither generally,or specific to Mary or Elizabeth.
I also found both labor scenes just a little too pedestrian for an event like the birth of Jesus,or to a lesser degree,John.