What are the rights of a father who abandoned his children and married another woman as an act of revenge against their mother?

Allah Almighty commanded kindness and dutifulness to parents. This includes the father, even if he falls short in his children's rights, for his shortcomings are not a justification for undutifulness or ill-treatment towards him.

Children must honor their father and treat him kindly by all means. If they are able to advise him and remind him of their rights, that is better. They can also seek help from someone who holds a position of respect with the father to advise him to fulfill his duties and remind him of the prophetic traditions that warn against neglecting obligatory maintenance, such as his (peace and blessings be upon him) saying: "It is sufficient sin for a person to withhold from one whose sustenance he possesses," and "It is sufficient sin for a person to neglect those whom he supports."