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 is His slave and Messenger.
In principle, a divorced woman who is in her waiting period should remain in her marital home and not go out of it as Allaah Says (what means): {Do not turn them out of their [husbands’] houses, nor should they [themselves] leave [during that period].}[Quran 65:1]
Besides, the Fiqh Encyclopedia reads: “The jurists agreed that it is not permissible to drive the divorced woman out of her marital home during her waiting period and it is not permissible for her to go out from the dwelling where she observes her waiting period except for a necessity.”
Moreover, the jurists said that it is not permissible for her to go out whether or not her husband gave her permission because this is among the rights related to the waiting period which is the right of Allaah, so it is not permissible for the husband to eliminate any right related to it in the same way he is not permitted to eliminate the waiting period itself. The jurists also stated that a woman in her waiting period from divorce is not permitted to go for ‘Umrah even if her husband had given her permission to do so before divorcing her and that if he divorced her after giving her permission, then his permission becomes null.
Therefore, if we presume that your father had permitted your mother to go for 'Umrah and then he divorced her, then his permission has become null and she is not permitted to go (for Umrah). Rather, some jurists are of the view that if she assumes the state of Ihraam after she was divorced, it is not permissible for her to travel until her waiting period finishes. Al-Khateeb Ash-Shirbeeni from the Shaafi’i School of jurisprudence, said: “If she assumes the state of Ihraam for Hajj or for ‘Umrah, or for both Hajj and ‘Umrah, after her husband had divorced her or died either after having his permission before that or without his permission, then she is not allowed to go out whether or not she fears the time of the rituals of Hajj comes to an end. This is because the permission has become null in the first case (i.e. the case of divorce or her husband’s death) or because there is no permission at all in the second case."
Therefore, since your mother has not yet assumed the state of Ihraam and she did not travel yet, then it is not permissible for her to travel for ‘Umrah until her waiting period finishes.
Allaah Knows best.