Conflict can be subdivided into two major categories: internal and external. "I Stand Here Ironing" contains both, but the main conflict is internal.
The narrator is struggling with herself. She is trying to come to grips with what she sees as her failure as a mother. The iron that "moves tormented back and forth" is symbolic of her tormented thoughts and her constant and repeated struggle to smooth the wrinkles from her daughter's life, a struggle that never seems finished no matter how hard she tries.
The external conflicts are the poverty and illness that interfere with the narrator's ability to successfully parent her child and the pending meeting with the counselor or teacher who has requested a meeting to discuss Emily. This request intitiates the internal conflict and creates an inner dialogue of accusations and excuses in the narrator.
The setting is more in the narrator's mind and deals with this internal struggle than in the physical appartment/house where the narrator is ironing.
The turning point, I think, occurs when the narrator decides that she should just let Emily be, when she realizes that Emily is not an utter failure and that, although she may never reach her full potential, she will survive and possibly thrive. But even after this decision, the reader is left with the feeling that the internal struggle is not over, that like ironing, it returns and is never really finished. The mother hopes that Emily realizes ''that she is more than this dress on the ironing board, helpless before the iron."
In other words, she hopes that Emily will learn that she doesn't have to conform and that she doesn't have to be what the world dictates she become. She hopes that Emily will not allow some outside force to shape her or crush her. As a mother, the narrator never finishes worrying about her child. And as the mother of an often troubled or struggling child, she never truly finishes blaming herself.
Below are some links that more specifically discuss the characters, style and themes of "I Stand Here Ironing."