Must one give money to the mother for the sister to hold a mixed and unlawful wedding, knowing that the sister will not observe hijab, and is not submitting to the mother’s request considered an act of disobedience?

You are not obligated to pay for a wedding celebration that includes forbidden acts such as intermingling (of sexes), as this is considered cooperation in sin and transgression, which is prohibited by Islamic law. This is not considered disobedience to parents (Uquq), for there is no obedience to a creature in defiance of the Creator. It is preferable to help your sister establish her home. You should advise your mother and sister to abandon forbidden acts such as immodest dress and intermingling, and this advice should be given with gentleness and kindness.