All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The preponderant scholarly opinion in this regard is that making such a vow is disliked. This is because it neither hastens nor delays anything that is predestined by Allaah Almighty. Ibn ‘Umar narrated that the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said: "A vow neither hastens nor defers anything (that is predestined), rather, it is a means whereby (something) is extracted from the miserly person." [Muslim]
However, if someone has already made a vow, it is incumbent on him to fulfill it, unless it is a vow to do an act of disobedience to Allaah, the Exalted. ‘Aa’ishah reported that the Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever vowed to obey Allaah, the Exalted, must obey Him; and whoever vowed to disobey Allaah, the Exalted, must not disobey Him." [Al-Bukhari]
Hence, it is incumbent upon this woman to fulfill her vow. However, given that she is now unable to fulfill her vow in the manner that she intended when making it, it is permissible for her to offer the monetary value of the jewelry based on the price of gold at the time when her daughter recovered from her illness (i.e. when the condition, upon which she had rendered her vow conditional, was fulfilled).
Allaah Knows best.