。
She took very kind care of my child.
Literal
She [topic-は] my child [object-を] very kindly care-did [for-me-てくれた].
世話してくれた compresses the noun + する pattern by dropping the を between 世話 and する, treating the whole as a unified verb — slightly more compact and casual than 世話をしてくれた. 親切に is the adverbial form (na-adjective + に) of 親切 ('kind'). The combination of past tense and the benefactive ~てくれた expresses heartfelt past gratitude — the speaker is reflecting on a kindness already received.