Is it obligatory to continue financially assisting one's older brother, knowing that the money might be given to his disobedient children?

If your brother's children use the money for sinful acts, then it is not permissible to help them. However, if they spend it on permissible matters, then there is no harm upon you. You should advise them, enjoin them to good, and forbid them from evil, for perhaps your kindness will be a reason for them to accept your advice.