Must parents obtain their daughter's consent before accepting a proposal?

Yes, a daughter's consent is very important, and for a previously married woman it must be given explicitly.
The Prophet ﷺ said: "A previously married woman is not married until she is consulted (explicitly), and a virgin is not married until her permission is sought." When asked how a virgin gives permission, he answered: "Her silence." Khansa' binti Khidham, whose father married her off without her consent, complained, and the Prophet ﷺ annulled that marriage. Accepting a proposal on a daughter's behalf without asking can lead to an engagement that has to be broken off later. Under Islamic family law in Malaysia, the consent of both parties is also required to register the marriage. See the marriage guardian (wali).