In movie The Woman in Black the key issue with attorney Arthur Kipps is his inability to accept the death of his young wide, Stella. Much differently than in the book, in the movie Arthur's son, Joseph, survives his mother, who dies at childbirth.
Hence, Arthur develops another issue that stems from his wife's untimely death, which is his lack of connection to his son. This is the reason why Arthur is characterized in the movie as a busy man who depends entirely on his governess to care for his son because, otherwise, he his unable to connect with him in any other level.
When Arthur goes to Crythin Gifford, the movie makes it look as if the situation going on with the children of the village, where they have been dying at the sights of the woman in black, will affect Arthur's own situation with his child. It is true, however, that there is some sort of connection that Arthur does build with Joseph eventually. The arguable final proof of the moment when Arthur and Joseph come to a point of unity is when Arthur realizes that the woman will go after his son, he rushes to be with him, and they eventually will die together at the train tracks.
Yet, there is more to his characterization. Arthur is depressed almost to the point of illness. He appears to be suffering from post traumatic stress, and he hallucinates about his wife while, at the same time, he has lapses of vivid memories of the moment of her death. He does not act tenderly toward his son and reflects in his behavior a slight hint of resentment.
These actions change toward the end right before they both die.