Praise be to Allah
There is nothing wrong with a woman wearing whatever kinds of clothes she wants at home, of clothes that women in her country usually wear at home, so long as she is safe from non-mahram men being able to see her. Hijab has only been prescribed in order to conceal women from non-mahram men, as Allah, may He be exalted, says (interpretation of the meaning):
“O Prophet! Tell your wives and your daughters and the women of the believers to draw their cloaks (veils) all over their bodies (i.e., screen themselves completely except the eyes or one eye to see the way). That will be better, that they should be known (as free respectable women) so as not to be annoyed. And Allah is Ever Oft-Forgiving, Most Merciful”
“…and not to reveal their adornment except to their husbands, their fathers, their husbands fathers, their sons, their husbands sons, their brothers or their brothers sons, or their sisters sons, or their (Muslim) women (i.e. their sisters in Islam)…”
So it is permissible for them to show their adornment in front of their husbands and mahrams. Therefore it is more appropriate that this be permissible when the woman is on her own.
Based on that, there is nothing wrong with a woman uncovering her head whilst cooking and doing other things, if she is alone in the house and is safe from non-mahram men being able to see her.
But she must observe full shar‘i hijab when she is in the presence of non-mahram men, whether that is inside the house or outside.
For more information on the definition of a woman’s ‘awrah in front of other women and her mahrams, please see fatwa no. 82994
And Allah knows best.