Is a father obligated to fulfill a vow to slaughter an animal if he swore an oath in a state of anger, knowing that the vow was about preventing his daughter from going to university, even though she committed no sin, and he later acknowledged this?

Your father's vow is considered an oath of obstinacy and anger, and like an oath, he has the choice between fulfilling it or breaking it. In the latter case, he must offer expiation for an oath or perform what he vowed. If you go to university, your father has the choice between offering expiation for an oath or slaughtering the animal. Your father's anger does not exempt him from accountability unless he completely lost his mind, as the majority of jurists hold that an angry person is accountable for his actions. You must denounce your sister's action, because arguing with and disobeying a parent is forbidden, and compelling him with an argument is considered disobedience.