She made an oath dependent on some matter, and that matter is no longer an issue; what is the ruling?

As with all other commitments that a Muslim takes upon himself, oaths are based on the intention and purpose of the one who made the oath, because the basic principle is that matters are judged by their purpose. From this is derived the principle that the purpose (meaning) of the words depends on the intention of the speaker.

Al-Ashbaah wa’n-Nazaa’ir by as-Suyooti (1/81).

The basis of this is the hadith of the Messenger of Allah (blessings and peace of Allah be upon him): “Actions are but by intentions, and each person will have but that which he intended.” Narrated by al-Bukhaari (1) and Muslim (1907).

Ibn ‘Abd al-Barr (may Allah have mercy on him) said:

The basic principle with regard to this matter – i.e., oaths – is to pay attention to what was intended by the one who swore the oath. If he did not have any particular intention, then we should look at the story behind it [i.e., the reason why he swore the oath], and what provoked him to swear the oath, then judge the matter on the basis of what is usually the case with his peers.

End quote from al-Kaafi (1/452).

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:

They [the scholars] are unanimously agreed that with regard to oaths, reference should be made to the intention of the one who swore the oath, if the wording could be understood in that way.

End quote from Majmoo‘ al-Fataawa (32/86).

Based on that, there are two possibilities with regard to your mother’s oath:

The first possibility is that her aim was that you should attend this occasion with your hair long, without having been cut. Based on that, so long as the occasion was cancelled, then there is nothing wrong with you cutting your hair, and she does not have to offer any expiation, because the reason for the oath is no longer applicable.

Ibn al-Qayyim (may Allah have mercy on him) said:

If the Lawgiver made a ruling dependent on some cause or reason, then the ruling ceases to apply when that cause or reason is no longer applicable… sharee‘ah is based on this principle.

Similarly, if someone swore an oath not to do something for a particular reason, then that reason ceases to be applicable, then he does not break the oath by doing it, because his oath was dependent upon that reason. Therefore if the reason is no longer applicable, the oath is no longer applicable.

End quote from I‘laam al-Muwaqqi‘een (5/528-529).

The second possibility is that your mother’s aim was that your hair should be left long for the duration of this period, and the aim was not the particular occasion.

Based on that, you have to look at the date that was set for the occasion that was cancelled, and not cut your hair before that period of time has elapsed, then after that you can cut your hair.

And Allah knows best.