Is the father entitled to custody of his children after the mother remarries, and what is the solution to reconcile the father's right to see his children with the mother's desire to raise them well, taking into account the current marital disputes?

It is not permissible to prevent a father from seeing his children, and a father has the right to their custody if he is just, meaning not known for immorality. It is recommended to resolve the issue through understanding with the current husband and the former husband, and by referring to the Islamic Center.