Final answer:
The excerpt from 'At School Abroad' that most clearly explains why Brontë was unhappy with the Sidgwicks but is happy with the Hégers.
Step-by-step explanation:
The excerpt from At School Abroad that most clearly explains why Brontë was unhappy with the Sidgwicks but is happy with the Hégers is: 'There came a time when no words passed between Jane and her women. Silently they went about their household duties, and secretly they went about the underhand work to which they had been bidden. The gloom of the house and the gloom of its mistress, which darkened even the bright spirit of little Fay, did not pervade these women.'
This excerpt shows that Brontë was unhappy because the Sidgwicks created a gloomy and oppressive environment in the house, which affected not only Jane but also the others living there. In contrast, Brontë is happy with the Hégers because they do not bring the same gloom and that they also create a more positive and supportive atmosphere.