Is a woman sinful if her husband's brothers see her without a hijab unintentionally, knowing the ruling on the niqab, given that she cannot wear it all the time due to hardship, lives with them in the same house with shared facilities, and her husband refuses to move to their own apartment?

It is the wife's right to have an independent dwelling with its facilities, including a kitchen. The husband does not have the right to prevent her from using her private kitchen or compel her to use his family's kitchen. Furthermore, the woman must cover her face from her husband's brothers. If she diligently endeavors to avoid them seeing her with an uncovered face, then there is no sin upon her if one of them sees her unintentionally. It is also important to warn the brothers against suddenly entering upon their brothers' wives.