Is he considered mistaken for refusing to approve his sister's removal of the hijab for the sake of marriage, and what is his legal (Shar'i) position on that?

If the intent is to remove the hijab in front of the suitor, then there is no harm in that. However, if the intent is to remove it permanently in front of non-mahram men, then it is not permissible. You are permitted to denounce this evil. If you are unable to change it, then you should leave the house at the time this evil act is being committed.