We never actually find out how Betty's mother died. However, it's perfectly understandable that Betty would cry out for her mother in a time of stress and fear; this is quite a common reaction, especially among small children. Betty has been lying completely still, pretending to be unconscious. This is her way of dealing with the unpleasant experience of the strange ritual in the forest in which she found herself involved. As well as being worried about what might happen if her dad discovers what she's been up to, Betty's terrified of Abigail. (And who wouldn't be?) It's right after Abigail threatens to beat Betty that she "wakes up" screaming and calling for her mother. This is exactly the kind of reaction we might expect from a frightened, confused ten-year-old child who's just been threatened with physical violence.

In reality, Elizabeth Parris, Betty's mother was still alive throughout the trials.  However, Miller chooses to portray Rev. Parris as a widower perhaps to explain Betty's freedom to run around with Abigail and the older girls and participate in their schemes.

In real life, Elizabeth Parris was an invalid, and Betty was a sickly child.  She often was confined to bed or prevented from doing household chores, so she would have been especially interested in hearing Tituba's exciting tales as a diversion.

In The Crucible Miller does not mention the cause of Elizabeth Parris's death; he simply describes Parris as a widower in his opening notes.  If Miller just intends for the audience to believe that Elizabeth died from her chronic illness, this would have frightened Betty because, as a bed-ridden little girl, she would most likely think that she was going to endure a life of illness and an early death as her mother had.