Why does Doyle include Helen's family life before and after her mother's death in "The Adventure of the Speckled Band"?
Doyle does this in order to build up a full picture of Helen's life, in particular the baleful influence of her stepfather over her and her twin sister Julia. The picture that we get of her stepfather, the fearsome Dr Roylott, is indeed a grim one and provides an early hint that he is in some way responsible for Julia's terrible death. We are given the background to the Roylott family, apparently one of the oldest families in England, which however became impoverished and dissolute in the last hundred years. Helen also speaks of the 'hereditary mania' that afflicts male members of the family, and her belief that Roylott also suffers from this. Certainly, he appears disposed to acts of violence from the first, and after taking her stepdaughters to live with him in the hereditary family seat at Stoke Moran, he generally shuts himself up. When he does come out, it is usually only to get involved in a brawl of some kind.
Doyle, then, gives us a full picture of the sombre conditions under which the girls lived. It seems that things got worse after the death of their mother, whom Roylott had married in India; she was killed in an accident soon after the family returned to England. Although Roylott appears to have no redeeming features whatsoever, and plans to kill his daughters simply for the sake of the money left to them by their mother, it may be that their mother's death affected him emotionally, and helped drive him over the edge.
In view of her grim family life, culminating in the death of her sister, it is no surprise that Helen Stoner in a state of extreme anxiety, as is clear from the following description:
She raised her veil as she spoke, and we could see that she was indeed in a pitiable state of agitation, her face all drawn and grey, with restless frightened eyes, like those of some hunted animal. Her features and figure were those of a woman of thirty, but her hair was shot with premature grey, and her expression was weary and haggard.
Helen's terrible experiences, then, have aged her, reduced her to a 'pitiable' state of nervousness. Thanks to her foresight in consulting Holmes, however, she will escape the dreadful fate that overtook her sister.