Is a woman allowed to sit in her house with her hair exposed?
If there are no non-mahram men, then a woman can expose her head in the house.
(Hazrat Mufti) Yusuf Ludhyanvi (May Allah have mercy on him)
Aap ke Masaail aur unka Hall Vol.8 Pg.67
A woman asked a detailed question about wearing a scarf when working at home, Mufti sahib answered in the following manner:
The good thing is for a woman not to expose her head. However, if there are no non-mahrams at her house, then it is permissible to expose the head. It is not permissible in front of non-mahram men.
Aap ke Masaail aur unka Hall Vol.8 Pg.64
Also see here.