It could be that Hermione did something that she thought was right in the wizarding world's politics or magic use, but it went against the Weasley family's traditional values that Mrs Weasley holds dear. Like Hermione might have supported a new law that would change the way pure - blood and half - blood wizards are treated, and Mrs Weasley thought it was too radical.
Maybe Hermione made a decision regarding Ron that Mrs Weasley didn't approve of. For example, if she rejected Ron's marriage proposal in a rather harsh way, Mrs Weasley, who was very fond of Hermione as a potential daughter - in - law, could be extremely disappointed and angry.
Hermione could be very hurt. She respects Mrs Weasley a great deal, and to receive such an angry message from her would be a big blow. So she might cry and isolate herself for a while to think about what she did wrong and how to make it right.
It could be that Hermione's Howler contained something really hurtful or embarrassing that made Mrs. Weasley emotional and shed tears.
It's possible that the content of the Howler conflicted with Mrs. Weasley's expectations or values for Hermione, causing her distress and resulting in tears. Another reason could be that it brought up past issues or tensions that were unresolved and finally boiled over.
A great Hermione stands up to Mrs Weasley fanfiction would incorporate the magical world's backdrop well. It could be set during a big family gathering at the Burrow. Hermione might stand up because of a difference in opinion about how to handle a magical creature situation. The author should also explore the emotions of both characters - Hermione's determination and Mrs Weasley's shock or disappointment, and how they resolve those feelings.
One possible reason could be that Mrs Black's old - fashioned pure - blood views conflict with Hermione's more inclusive and progressive ideas. Hermione, being a Muggle - born witch, might not tolerate Mrs Black's snobbish and discriminatory remarks about non - pure - blood wizards and witches.
One scenario could be that Hermione is being bullied by some pure - blood supremacists at Hogwarts for being a Muggle - born. Mrs Weasley, who has always been inclusive, finds Hermione crying in the library. She sits down with her, hugs her tightly, and tells her that her blood status doesn't define her worth. Mrs Weasley might also offer to teach Hermione some of the Weasley family's special spells to make her feel more confident.
Perhaps Harry is feeling a sense of guilt or shame. Maybe he's made a mistake that he doesn't want Mrs. Weasley to find out about, like using a dark spell in a moment of desperation during a battle. So, to avoid her motherly scrutiny, he starts to ignore her. He might be afraid that if she gets too close, she'll figure out what he's done and be disappointed in him.
I'm not sure of a specific 'Mrs Weasley comforts Hermione' fanfiction off - hand. However, you could try looking on Archive of Our Own (AO3). There are often many well - written fanfics in the Harry Potter fandom. Maybe in one fic, Hermione has a fight with Ron or Harry and Mrs Weasley, being the kind - hearted woman she is, takes Hermione under her wing and offers her some words of wisdom and a warm cup of tea to soothe her.
One possible reason could be that Harry is preoccupied with his own dark thoughts or problems. Maybe he's worried about Voldemort and his plans, and in his distracted state, he unconsciously ignores Mrs. Weasley's attempts to reach out. Another reason might be that he's trying to be independent. After years of being in the wizarding world on his own terms, he might not want to be mothered too much by Mrs. Weasley.
There's also a chance that she'll be hurt. Mrs. Weasley has a big heart and Harry ignoring her could really wound her. She might then become more withdrawn herself, focusing on taking care of her own family and leaving Harry to his own devices, while still secretly hoping he'll come around.