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 'alyhi wa sallam, is His slave and Messenger.
Fulfilling this vow is prohibited. The only thing this mother must do is repent to Allaah The Almighty.
The reason for this is because Hadhrahs are mainly composed of religious innovations and contain much evil, like poems that exaggerate the status of the dead and ask for their help, in addition to using musical instruments and dancing during the alleged performance of Thikr (mentioning of Allaah), and other evils.
With regards to women visiting the grave of As-Sayyid Al-Badawi:
firstly, scholars disagree about the ruling on women visiting graves in general. The majority of scholars consider it reprehensible. However, some scholars consider it prohibited.
As for visiting the grave of As-Sayyid Al-Badawi, it is absolutely prohibited because the visitor usually fails to denounce the evil committed there, namely the act of Shirk (polytheism) represented in people circumambulating around the grave, making vows, asking the deceased for help, and offering animal sacrifices. Moreover, there is a possibility that this woman may commit some of these prohibited acts there.
In conclusion, it is prohibited to fulfill this vow. Instead, this woman may give money to the poor, or offer an animal sacrifice to Allaah The Almighty and distribute its meat among the needy - it is absolutely prohibited for her to hold a Hadhrah or to visit the grave of As-Sayyid Al-Badawi.
Allaah Knows best.