Is it obligatory for the questioner's mother and sister to offer a sacrifice (hady) if they intend to perform Hajj after performing Umrah and exiting therefrom?

If Allah has not decreed Hajj for your mother and sister this year, then they do not owe a hadi (sacrificial animal) for performing 'Umrah (definition) in the months of Hajj, as the tamattu' (combination of 'Umrah and Hajj) has not occurred. And if Hajj is decreed for them, they still do not owe a hadi if they travel a distance for which prayer can be shortened after performing 'Umrah. This is according to the view of scholars who hold that if a mutamatti' (one performing tamattu') travels a distance for which prayer can be shortened after 'Umrah, the dam at-tamattu' (sacrifice for tamattu') is waived if he performs Hajj mufrid (singly, without combining with 'Umrah).