I started by looking at what the bones of the story are. There are lots of variants, but the most common one is that:
1) She is poor but haughty. Her beauty interests the local men, but she rejects them.
2) She determines to win a rich man (usually described as a ranchero.)
3) She marries him and has (usually two) children.
4) He goes back to his previous lifestyle, including ignoring her in favor of women of his own class.
5) In some versions, he still pays attention to his sons, while ignoring her, so she drowns her sons. In others, she thinks that getting rid of the children will give her the freedom to recapture his attention.
6) She then drowns herself. She wanders the area near the river, trying to retrieve her drowned children and weeping (hence, the name "La Llorona," the weeping woman).
What I picked up on from this was the idea of her abuse at the hands of her wealthy husband. I thought about what the other women in the village might think of her and how her attitude that she was better than the local girls of her class might make them unwilling to help. Then, she could be avenging herself on the women who didn't help her by killing their children, so they all become weeping women.
For a number of reasons, I abandoned that approach in favor of thinking of her instead as a woman who doesn't even seek help when she's abused. She knows that her attitude towards the people of her village was bad, so she doesn't feel she can ask for help. She's punishing herself almost from the beginning. It made sense to focus then on her attitude towards her own family. I gave her a father who had always given her whatever she wanted. My real breakthrough was giving her a sister who became the narrator. She starts out by explaining that, "She is called a lot of things - a murderess, a bruja, a witch. Most often they call her La Llorona, the weeping woman. But before she was any of those, I knew her as my sister, Maria."
Her mother died young, so Maria never really learned about motherly love. Her father was grieving and set no bounds. Her sister resented having to raise this spoiled brat.
I needed a way for her to meet the rich man, so I made her father a blacksmith and the rich man raise horses for his father's rancho. And Maria could be a bit wild, so he sees her the same way he sees the wild horses he loves to tame. And that explains a lot about their situation. Once he has broken her - via marriage and children - she's no longer of interest.
The drowning of the children is just a moment of madness, when she thinks of them as the obstacle to being who she was before the marriage. Her suicide makes psychological sense, then. "What have I done? I deserve to die myself," is pretty much her thought process in her overwrought state. I pulled in a part of some traditional versions by having St. Peter refuse to admit her to heaven without her children. Then it makes sense for her to continue searching for her children.
The thing I didn't do enough with was an obsidian necklace (hard and dark, reflecting her pre-marriage attitude). That necklace was the only thing of her mother's she had - and her possession of it was another reason her sister resented her. In the future, I need to have her husband break the necklace, so the scattered obsidian beads are a visible reminder of the shattering of what she was. The abuse is isolating and her ties to her mother are broken, which is what keeps her from asking her father and sister for help.
I think what I ended up with was reasonably successful, although not qutie where I wanted it to be. Stories have to be told to see what does and doesn't work. One problem with having the sister as a narrator is that she isn't omniscient. I just realized now that she can find some of it by finding a diary afterwards, as well as finding the obsidian beads. She may have to talk to her dead sister to find out about Saint Peter incident, though, which is still a bit problemmatic. If I tell it enough times, I will find a solution.