He used that way of saying - the deepest way of articulating some sort of loving words - only with his daughters (and his cows...)
Back on imdb I remember the idea with the omission of this endearment addressed to Jack in the reunion scene, yes had to do with the idea that it would be out of character a bit for film-Ennis, and because it would be hard to convey the idea that he only used "little darlin" to refer to his horses, daughters and Jack in the film.
Right Amanda, you're a very cute observer, and your observations are all very much punctual (as always). And I shall make a correction, as I stated "cows" while they were "horses". Sorry!