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.
Islam encourages that relationships among Muslims in general be in the best state of affinity and affection. This ex-couple should not forget their mutual graciousness, particularly since Allaah The Almighty granted them children who embody their bond. How could they commit these actions and Allaah The Almighty has enriched each of them from His abundance and helped each to remarry? So, both of them have to fear Allaah regarding one another.
However, if this woman arouses problems, invents lies against people and urges her children to hate their father, she is disobeying Allaah, wronging people, and seeking severance of kinship ties. All these actions are the work of Satan and his soldiers. It is obligatory to remind her of Allaah The Almighty.
Moreover, if her daughter conveys stories in order to spoil people's relations, she is committing tale-bearing which is one of the major sins as previously clarified in Fatwa 81748. She, too, has to be advised and warned against the bad consequences of her action in this life and in the Hereafter.
No doubt, people commit these actions because they are heedless of Allaah The Almighty, death and reckoning. Were a Muslim mindful of that, it would urge him/her to keep away from what displeases Allaah The Almighty. It is even worse that these evil actions are committed by old people, for they are supposed to set a good example for the children, not a bad one.
Nonetheless, these actions do not renounce any of the parents' rights to dutifulness. That is because the parent does not lose his/her right to the children's dutifulness due to disbelief, so it is with greater reason that he does not lose it for other reasons. For further information, see Fataawa 82254 and 84942.
Allaah Knows best.