Is a father considered sinful for abandoning his family despite their financial need for him, and for fleeing responsibility, knowing that the mother bears most of the expenses?

If the father is able to provide for his children but withholds maintenance despite their need, then he is sinful. However, if he is unable, there is no sin upon him.

It is not obligatory to leave the mother and reside with the father, but it is not permissible to abandon him, mistreat him, or neglect his care and visits. For the father's right is great and is not forfeited by his injustice.

It is obligatory for children to honor their father, visit him, and attend to his needs, especially when he is ill, and to beware of negligence or estrangement; for disobedience to parents is among the grave sins.

Honoring one's father and being kind to him are among the greatest means of attaining Allah's pleasure and entering Paradise, for the father is the middle gate of Paradise.