She had been thinking that she would become financially independent from her parents once she got into college.
Literal
She [topic-は] college [to-に] enrolled-when, parents [from-から] economically let-me-be-independent [intent-と] was-thinking.
A layered sentence with two clauses inside one thought. The conditional/temporal ~たら sets up 'once she enrolled.' The volitional 独立しよう ('let me become independent') gets reported via と思う as 'was thinking she would.' Past progressive 思っていた marks her sustained intention before the moment described. 経済的に ('financially') is the adverbial of 経済的 ('economic'), built by attaching に to a な-adjective.