Symbolism, Imagery, Allegory
Surprise, surprise—come on, they're in the title and all over the story, so you knew chrysanthemums were going to turn up here in the "Symbolism" section. We first see them when Elizabeth heads outside to look for her son, and the narrator notes:
Beside the path hung dishevelled pink chrysanthemums, like pink cloths hung on bushes. (1.3)
Hmm, disheveled? Not exactly the most flattering description . . .
Just a little bit later, John is picking at the chrysanthemums as they walk outside, and Elizabeth stops him because the raggedy bits of flower he's creating "look nasty" in her opinion (1.15). However, a moment later the narrator notes that:
She, suddenly pitiful, broke off a twig with three or four wan flowers and held them against her face. When mother and son reached the yard her hand hesitated, and instead of laying the flower aside, she pushed it in her apron-band. (1.15)
Hmm, interesting—maybe she's a bit fonder of the flowers than she lets on at first.
Later on, we get a little more insight about why Elizabeth blows hot and cold about the 'mums. Annie gets excited when she sees chrysanthemums tucked in her mother's apron and gushes about how great they smell, but Elizabeth isn't having it:
"No," she said, "not to me. It was chrysanthemums when I married him, and chrysanthemums when you were born, and the first time they ever brought him home drunk, he'd got brown chrysanthemums in his button-hole." (1.76)
Ah, we get it—if we associated the smell of something with a drunk spouse, we might not like it so much, either.
But wait, let's back up—in explaining why chrysanthemums give her bad vibes, Elizabeth lumps together getting married/having kids with her husband coming home fall-down (or can't-get-up) drunk. If she was trying to quash her daughter's enthusiasm for mums, that probably did the trick.
But let's back up even further and try to understand what's happening here. Sure, you might find it odd that Elizabeth associates the chrysanthemums with supposedly happy things like marriage and children, but think about it: she doesn't appear to be happy in her marriage now, and she probably associates chrysanthemums with all the hope and promise of her younger life that hasn't really panned out. Which also might explain why, even if she supposedly doesn't like the flower anymore, she's still compelled to grab a bunch here and there—she still remembers the nice memories, too.
In fact, as we learn when Elizabeth is arranging the parlor to accommodate Walter's corpse, she keeps a vase of chrysanthemums in the house. If she really hated the flower, why would she do that? Sounds like she's got way mixed feelings about that particular flower—and everything it represents to her, too.
Of course, we should also mention that chrysanthemums are often viewed as a symbol of death, so . . . yeah, that could definitely explain why they pop up super frequently in a story that, you know, revolves around a death.