Is the sister obligated to inform her father of her failure in a school subject, knowing that this might anger him, and is she required to fulfill her vow to inform him if she succeeds?

It is permissible for the sister to conceal her failure from her father, and perhaps that is better so as not to anger him. If she succeeds in the future, she has the choice between fulfilling the vow by informing her father or atoning for it with an expiation for an oath. However, if her vow was related to her success and has not yet occurred, then nothing is binding upon her.