Elizabeth Grimes is Gabriel's wife, and John, Roy, Sarah and Ruth's mother. She's a friend and sister-in-law to Florence, Gabriel's brother. Since most of these characters have serious conflicts with one another, Elizabeth finds herself caught in the middle of many different conflicts. She mostly manages to stay out of them herself, but does get caught in the crossfire when things get too violent.
Let's start with her relationship to Gabriel. This is the real gooey center of the molten conflict cake. Gabriel is a big jerkface, to put it nicely, and Elizabeth spends most of her time trying to smooth over the messes he creates.
When Roy complains about Gabriel's violence, she says that his father "beats you [...] because he loves you" (1.1.56). Uh, yeah, not too convincing, there, Lizzie. But it shows that she's trying to make the best of a bad situation.
Why doesn't she just leave? What makes Elizabeth stay put and make the best of things rather than hightail it? The key is her big secret: John is not Gabriel's son. John doesn't know it, and she doesn't want him to. She wants her eldest son, whose father died before he was born, to feel like he's part of the family, and so she tries to hold everything together.
One day, when Gabriel asks her if she's truly repented of her sin, Elizabeth stands up for herself:
"I know you ain't asking me to say I'm sorry I brought Johnny in the world. Is you?" And when he did not answer: "And listen, Gabriel. I ain't going to let you make me sorry. Not you, nor nothing, nor nobody in this world. We is got two children, Gabriel, and soon we's going to have three; and I aint' going to make no difference amonst them and you ain't going to make none either." (2.2.114)
Elizabeth is capable of distinguishing between the sin (as Gabriel understands it) of having premarital sex and the product: her beloved child, Johnny. She tries to make Gabriel see this difference, too, but knows that she has failed. So she sticks around to protect her kids from Gabriel, like a mother bear.