。
She grew up in a wealthy household.
Literal
She [topic-は] wealthy [genitive-の] household [in-に] grew-up.
育つ ('to grow up, be raised') is the intransitive counterpart to 育てる ('to raise'). The に here marks the place of growing up — the household as the locus of the formative process. 家庭 specifically denotes a household as a social/emotional unit (with its 家庭環境 'family environment,' 家庭料理 'home cooking'), distinct from 家 ('house' as a physical structure) and 家族 ('family' as a group of people).