How can one deal with a family that demands non-essential expenses and mistreats the eldest son and his wife upon refusal, knowing that the children believe their money belongs to their father?

Filial piety within what is considered righteous is obligatory. However, parents are not permitted to abuse their rights in a way that harms their children. If the parents are in need of money, it is obligatory for a wealthy son to spend on them. But if they have what suffices them, then spending is commendable (mustahabb) but not obligatory. As for supporting adult siblings, it is not obligatory for you, and your parents are not permitted to force you to do so, for wealth is not permissible unless given willingly by its owner. The hadith "You and your wealth belong to your father" does not mean absolute ownership by the parent, but rather permissibility under certain conditions.