Is a girl considered disobedient to her mother if she wears the niqab outside the home, knowing that her mother is not religiously observant and has sworn that the girl should not go out wearing it?

There is no obedience to a creature in disobedience to the Creator. Therefore, the hijab and covering the face and hands are obligatory. The primary effort should be to convince the parents of this. If conviction is not possible, then do not obey them in disobedience to the Creator. It is advised not to leave the house except out of necessity to avoid conflict with the mother if she insists on her opinion.