。
She's gradually been getting used to country life.
Literal
She [topic-は] gradually this countryside [possessive-の] life [to-に] is-getting-accustomed-to.
Three time-aspect layers stack here. ~に慣れる ('get used to X') takes に, parallel to many emotion/cognition verbs. ~てくる ('come to V, V over time') marks change accumulating up to the present — perfect for gradual adjustment. Then ~ている wraps the whole thing in the progressive, giving 'has been gradually getting used to.' Add 次第に at the front and the gradualness is doubly stamped. 田舎 ('countryside, rural area') often carries warm, nostalgic connotations in Japanese — but city-to-country relocation is a real adjustment.