。
She reluctantly agreed to our proposal.
Literal
She [topic-は] our proposal [to-に] reluctantly agreed.
しぶしぶ is one of Japanese's rich crop of 擬態語 (state mimetics) — words that describe a state, manner, or feeling without imitating any actual sound. It paints reluctant, foot-dragging compliance: she said yes, but only after some inner resistance. 同意する ('to agree, consent') takes its object with に, just like 応じる, 賛成する, and other agreement verbs. The sentence as a whole has the slightly stiff feel of a written report — the kind of phrasing you'd see in a meeting minutes or a journalistic summary of a negotiation.