Is it obligatory to fulfill a vow by slaughtering a sheep this Eid al-Adha, or should one wait for the gathering of siblings and family, knowing that this gathering has not taken place for four years?

The vow must be fulfilled in the manner in which its owner vowed it. Since the questioner stipulated the gathering of relatives to fulfill her vow, and this has not yet happened, she is not obligated to fulfill it until the condition is met. There is no harm in delaying it for the mentioned period due to the condition not being met, but there is no harm in expediting its fulfillment this year even if they do not gather. Therefore, it is preferable to hasten to fulfill the vow on the earliest Eid to clear one's conscience. As for the Udhiyah (sacrifice), it is required every year regardless of the vow.