What is the Islamic legal ruling on dealing with a father who asks his children for money, knowing that their mother was the one who raised them, and the father supports another wife and her relatives, while the children are taking care of their mother and younger brother?

The father's maintenance is obligatory upon the son if the father is poor and does not possess what suffices him. This obligation is not waived by the father's shortcomings towards his children. However, if the father is wealthy, then maintenance is not obligatory upon him, but it is commendable for the son to spend on him out of filial piety and in hope of reward, for "the Lord's pleasure is from the parent's pleasure, and the Lord's wrath is in his wrath." Part of honoring one's parents is to give them money, even if they are not in need.