All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Hijab is an obligation upon a Muslim woman and she is obliged to abide by it and not be negligent about it in any case. There is no obedience to the parents in not wearing Hijab because obedience is required only in what is permissible and there is no obedience to a creature in disobeying The Creator. For more benefit, please refer to Fatwa 84523.
However, it is not a condition that Hijab be a specific dress, but there are some characteristics that the Hijab should meet, and if they are met, the dress is Islamic [Sharee’ah-compliant]. For details on these characteristics, please refer to Fatwa 83702.
Hence, it is not permissible to obey the parents in any dress that does not meet all the conditions of Hijab as we already discussed.
As regards wearing the Abaayah which you referred to in the question, then if your parents do not have a sound reason for objecting to you wearing it, it is not an obligation to obey them in not wearing it because the obligation to obey one’s parents is not absolute; rather it is only in matters in which there is hardship on them when disagreeing with them and there is no harm on the children when agreeing with them, as stated by the scholars .
In any case, you should not make wearing such kind of dress a cause of dispute with your parents as this may lead them to prevent you from wearing Hijab entirely.
Allaah Knows best.