It should be noted that vows are not allowed. The Prophet (peace and blessings of Allaah be upon him) forbade them when he said: “They do not bring any good.” Hence some of the scholars are of the view that vows are haraam. Why should you make a vow? Why should you burden yourself? Will Allaah not heal you or your relative unless you stipulate conditions for Him? Subhaan Allaah! Do not make vows, rather ask Allaah for healing. If Allaah wants to heal him, He will heal him whether you make a vow or not. If you do that and you make a vow, if it is a vow to do an act of worship then you are obliged to fulfil it, because the Prophet (peace and blessings of Allaah be upon him) said: “Whoever vows to obey Allaah, let him obey Him.”
Based on this, we say to the woman mentioned in the question: You have to go for Hajj, but start with the obligatory Hajj, then do the Hajj that you vowed to do, because it is obligatory for you, and if you do not do it you are exposing yourself to a grave punishment which Allaah mentioned in the verses where He says (interpretation of the meaning):
“And of them are some who made a covenant with Allaah (saying): ‘If He bestowed on us of His Bounty, we will verily, give Sadaqah (Zakaah and voluntary charity in Allaah’s Cause) and will be certainly among those who are righteous.’
76. Then when He gave them of His Bounty, they became niggardly [refused to pay the Sadaqah (Zakaah or voluntary charity)], and turned away, averse.
77. So He punished them by putting hypocrisy into their hearts till the Day whereon they shall meet Him, because they broke that (covenant with Allaah) which they had promised to Him and because they used to tell lies”
They vowed that if Allaah made them rich, they would give in charity and would be righteous. Allaah gave them that, but they were stingy with the money and turned away from righteousness. “So He punished them by putting hypocrisy into their hearts” – until when? “till the Day whereon they shall meet Him” i.e., until death. “because they broke that (covenant with Allaah) which they had promised to Him and because they used to tell lies.”
In conclusion: beware of making vows, and if you do not make vows you will be fine. Do not oblige yourselves to do things that Allaah has not obliged you to do except as the result of your own actions. If a person has a sick loved one, let him say, “O Allaah, heal him.” If he wants to sit an exam, let him say, “O Allaah, grant me success,” because some students, when they find their studies hard and are afraid that they will fail, promise Allaah that they will do various acts of worship if they pass the exams. Then when they pass the exams, they start to ask questions and come to the scholars asking for a way out from the vow, but there is no way out and no other option than to fulfil the vow. End quote.