Is money taken without the father's knowledge to cover family expenses—given his failure to adhere to the agreed-upon wage—considered ill-gotten (haram) wealth, and is the one who takes it deemed disobedient to Allah?

If you are working as a hired hand for your father, he does not have the right to withhold the agreed-upon wages from you except for a just cause. If he refuses to give you the wages without a valid reason, you are permitted to take from his money an amount equivalent to your share of those wages without sin. However, beware of taking more than the amount of your wages, as that would be a sin and a forbidden excess that must be returned. Also, beware of mistreating your father, as this is an act of disobedience. It is the father's right that his son treats him kindly, even if the father wrongs him.