Q. Does a woman from a Chassidik background that due to her tradition of Tzniyus and modesty usually goes out from the house covered completely, however, when at home she only covers as Halacha requires have to behave the same way, covering herself completely and properly when she is present only before Non-Jews (they are building workers at home) since after all this is not a one of the Seven Mitzvot they have to keep?
A. Horav Aharon Miller’s Shlit’a opinion is that she should behave in front of Gentiles in the same way as she would when facing Jewish men.
Talmud (Yuma 47a) relates that "Kimchis had seven sons, all of whom merited to serve as Kohanim Gedolim, (High Priests). The Sages asked her, 'What have you done to merit this?' She answered them: 'The rafters of my house have never seen the braids of my hair.' " Kimchis covered her hair all the time even when she was alone inside her house.
As is obvious from the story, Kimchis ways were over what is normally required.
Horav Shlomo Miller’s Shlit’a opinion is similar.
Rabbi A. Bartfeld as revised by Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu Shlit'a