Aside from Homer, what other characters or forces are in conflict with Miss Emily in "A Rose for Emily"?

Miss Emily Grierson is in conflict with her family history, her culture, and time.
Family history
In the exposition of Faulkner's haunting story, Miss Emily is introduced as a "fallen monument" whose "august name" will join those others in the "cedar-bemused cemetery" who fought for the Old South. Clearly, then, she is burdened with her name and the noblesse oblige attached to it.
As part of this history, Miss Emily has lived under the patriarchy of her father and been both prevented from certain opportunities like marriage, which would offer her freedom from the burden of her family name.

We had long thought of them as a tableau; Miss Emily a slender figure in white in the background, her father a spraddled silhouette in the foreground, his back to her and clutching a horsewhip, the two of them framed by the back-flung from door.

Symbolic of this patriarchal repression, also, is the crayon portrait of Emily's father resting on the fireplace behind Miss Emily when she confronts the aldermen over her taxes, contending that she pays no taxes. For, although her father's allies are now dead, Miss Emily yet lives in this patriarchal past. In fact, when some ladies called upon Miss Emily the day after her father's death, she insisted he was not dead. Afterwards, the narrators comment, "and we knew that with nothing left, she would have to cling to that which had robbed her, as people will."
Furthermore, after Homer Barron leaves town, the narrators remark that "it was to be expected, too." For, again,

that quality of her father which had thwarted her woman's life so many times had been too virulent and too furious to die.

Her culture
Having lost the opportunity of marriage as a young woman, Miss Emily Grierson finds herself in conflict with her culture in which women are married much earlier than her age, so she settles for Homer Barron, a lower class man and a "Yankee." The townspeople are shocked when they observe their "monument" riding on Sunday in the "yellow-wheeled buggy" (the color yellow often symbolizes corruption). At first, the ladies of town mitigate the significance of Miss Emily's actions, arguing that a real lady would not "forget noblesse oblige--without calling it noblesse oblige."
Miss Emily continues seeing Homer, however, and she holds her head high in defiance as though

she demanded more than ever the recognition of her dignity as the last Grierson; as if it had wanted that touch of earthiness to reaffirm her imperviousness.

Clearly, Miss Emily acts in defiance of her position in this town that clings to much of the traditional culture of the Old South. The townspeople are also shocked by her purchase of arsenic. Rumors spread about her, as people believe she is contemplating suicide. Miss Emily is defeated in her defiance as she withdraws from society, and her front door remains closed for years.
Time
With the closing of her door, Miss Emily retreats from time. In her effort to stop its progression, however, Miss Emily arrests the departure of Homer in a perverse conflict. Years later, the townspeople enter the Grierson home after Miss Emily's funeral. In the upstairs bedroom, they discover a tarnished silver toiletry set; on the bed there is a decayed skeleton, and upon the second pillow in which there is an indention one long-grey hair rests, evidence of Miss Emily Grierson's "perverse" struggle to stop time.