How can one deal with a bad-tempered father who harms his children and wife and does not provide for them, while still desiring to please Allah and not disobey Him?

It is not permissible to raise one's voice at a father, for his right is great and is not forfeited by his wrongdoing. Allah has commanded to accompany parents with kindness, even if they enjoin shirk. It has been authentically reported from Ibn Abbas (may Allah be pleased with them both) that honoring parents is obligatory even if they wrong you. It is recommended to be patient and seek Allah's help, to advise the father gently, and to make abundant supplications.