In "The Horse Dealer's Daughter," what is Mabel's relationship with her family and feelings towards her parents?

It is clear from the ways in which her brothers treat her and discuss her future without compassion or care that Mabel does not occupy a very good position in the family of which she is a part. At the beginning of the story, when she and her three brothers are together for what may well be the last time whilst they overlook the dissolution of their family and their belongings, the brothers discuss what she might do without really including her in the conversation, and mention possibilities that would be obviously unpalatable to her, such as she might get work as a "skivvy" or a menial worker. Even Malcolm, the youngest of the brothers, who suggests that Mabel trains as a nurse, is ignored, as the text explains:

But Mabel did not take any notice of him. They had talked at her and round her for so many years, that she hardly heard them at all.

Mabel therefore has been in the position of having been talked "at" and "round" in demeaning and upsetting ways that she has ceased to even register their words or take notice of what it is that they actually say. It is clear from the brothers that whilst they are happy to discuss what she could do as something of an abstract question, they will not do anything for her, and she must make her own way in the world, indicating that their love and affection towards her is profoundly limited.

What kind of person is Mabel, and how does she relate to her brothers in The Horse Dealer's Daughter?

In D.H. Lawrence’s story, Mabel is a young woman who is living with three adult brothers after their parents have died. They are all facing a major upheaval because they all must leave the ranch; even selling the furniture would generate almost no income. Her self-centered brothers have made their plans independently and have not helped her at all. They take her for granted, and insult her with the nickname of “bulldog.” Mabel is in a severe predicament because she has nowhere to go. As the only sister, Mabel has assumed all the homemaking responsibilities, so she might be able to find work in service. She barely listens to what her rough brothers say, as they always talk among themselves without including her.

When Doctor Fergusson pays a call on them, he notices how silently and passively she sits among them. She has also gotten used to hiding her feelings from her brothers, so she does not share her intention with them; she just walks away and into the pond. Through serendipity, it is the doctor who prevents her suicide by pulling her out of the pond reveals a completely different side of her. Her negativity evaporates, and the passionate person she has been suppressing comes bursting out.