How can one deal with a father who is negligent in his financial and emotional duties towards his children after his marriage, especially noting his differential treatment between his children from his first wife and his daughter from the second wife, which negatively impacts their psychological well-being?

The Sharia commanded justice among children and forbade showing favoritism between them. So, if a father favors one of his daughters and neglects the rights of his other children, he is mistaken. However, the father's right is great, and honoring him is one of the most important reasons for Allah's pleasure, while disobeying him is a cause for His displeasure. His right to be honored does not diminish, no matter what his state. It is obligatory to continuously honor the father and treat him kindly. He can be asked to be just and advised gently and politely, or one can seek help from someone who can advise him, while frequently supplicating for him.