Is the mother obligated to perform Hajj to fulfill the vow, or does her refusal to perform Hajj nullify the vow for the one who made it?

A vow is an undertaking to perform an act of devotion that is not legally binding by Shar'ia, and it is not valid unless expressed verbally. If what the questioner said was an oath, by saying: "By Allah, I will do such and such," then expiation for breaking an oath is due if he breaks it. However, if he uttered the formula of a vow, then he must fulfill it as long as it is a vow of obedience, based on the saying of the Prophet, peace and blessings be upon him: "Whoever vows to obey Allah, let him obey Him; and whoever vows to disobey Him, let him not disobey Him." If he is unable to fulfill the vow, then expiation for breaking an oath is due.