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 ‘alayhi wa sallam, is His slave and Messenger.
It is sufficient for the head of a household to slaughter one sacrificial animal on behalf of himself and the members of his family upon whom he spends. So the sacrificial animal offered by your mother does not include her children mentioned in the question, for she does not spend on them and they do not live with her. As for offering one sacrificial animal on behalf of herself and her dead husband or offering one for herself and another one for him, this is permissible.
Allaah Knows best.