Is vowing to fast continuously until the need for facilitating the sister's marriage is met considered a transgression and a defiance of God, as the sister concerned mentioned?

The sister's vow is a vow of obedience, and she must fulfill her vow by fasting until Allah fulfills her need. If she is unable to do so, she must offer expiation for breaking an oath. She is not permitted to fast on Eid days, nor during menstruation or postpartum bleeding.