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, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
According to the majority of scholars, no Zakah is due on the jewelry of a woman that she uses for adornment purposes as mentioned in the Fatwa you read. What you mentioned regarding your wife's intention to sell her jewelry to complete the expenses of Hajj does not change it from being jewelry used for adornment upon which no Zakah is due. This is so because she does not intend to sell it for trade purposes. Moreover, she made the selling conditional on having money that helps her perform Hajj, which is a thing that has not yet happened as appears from your words.