Allaah has mentioned, in His Book, the men before whom a woman is permitted not to observe hijaab. Allaah says (interpretation of the meaning):
“And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts) and not to show off their adornment except only that which is apparent (like both eyes for necessity to see the way, or outer palms of hands or one eye or dress like veil, gloves, headcover, apron), and to draw their veils all over Juyoobihinna (i.e. their bodies, faces, necks and bosoms) and not to reveal their adornment except to their husbands, or their fathers, or their husband’s fathers, or their sons, or their husband’s sons, or their brothers or their brother’s sons, or their sister’s sons, or their (Muslim) women (i.e. their sisters in Islam), or the (female) slaves whom their right hands possess, or old male servants who lack vigour, or small children who have no sense of feminine sex. And let them not stamp their feet so as to reveal what they hide of their adornment. And all of you beg Allaah to forgive you all, O believers, that you may be successful”
For more details please see Question no. 5538.
Since the husband of a maternal or paternal aunt is not mentioned in this verse, the ruling is that the general principle of observing hijab in front of him applies in this case, unless this woman (the aunt) had breastfed her brother’s child, in which case her husband would be regarded as a father to her through radaa’ah (breastfeeding), in which case he would be a mahram for her. So if you did not breastfeed this niece, then she has to observe hijaab in front of your husband, in obedience to the command of Allaah, which is best for both parties. That is purer for the hearts and furthest removed from fitnah (temptation). We ask Allaah to reward you and your husband with good for taking care of this girl and bringing her up, and that He will cause that to weigh heavily in the balance of your good deeds.
Sheikh Muhammed Salih Al-Munajjid