Praise be to Allah.
Free mixing between men and women is haraam, because of the many negative consequences that result from it. The evidence for the prohibition on free mixing has been explained previously in the answers to questions no. 1200 and 97231, which explains that in most cases mixing is not free of haraam gazes, touching, being alone with a member of the opposite sex, infatuation or soft speech. This is what makes it haraam, not merely men and women being together in the same place, as they are together in the mosque or during tawaaf.
It is not permissible for a woman to take off her hijab in front of her husband’s brothers or their sons, or the paternal uncles of the husband or their sons, because they are not mahrams for her; rather they are strangers (non-mahrams) to her. The Prophet (blessings and peace of Allah be upon him) said: “Beware of entering upon women.” An Ansaari man said: O Messenger of Allah, what about the in-law? He said: “The in-law is death.” Narrated by al-Bukhaari (4934) and Muslim (2172). Al-Layth ibn Sa‘d said: The “in-law” is the husband’s brother and other similar relatives of the husband, such as his cousin and so on.
An-Nawawi (may Allah have mercy on him) said in Sharh Muslim: With regard to the Prophet’s words “The in-law is death”, what is meant is that there is more fear with regard to him than anyone else, and evil is to be expected of him, and the fitnah (temptation) is greater because he is able to reach the woman and be alone with her without anyone denouncing that, unlike the case of one who is a stranger. What is meant by “in-law” (hamu) here is the relatives of the husband apart from his father/grandfather and sons/grandsons. Fathers/grandfathers and sons/grandsons are mahrams for his wife and it is permissible for them to be alone with her. The word “death” here does not refer to them. Rather what is meant is the brother, brother’s son, paternal uncle, cousin, etc, who are not mahrams. People are usually careless about this matter and a man may let his wife be alone with his brother. This is what is referred to by “death” and should be prevented more than her being alone with a stranger for the reasons mentioned above. End quote.
Based on that, if your wife goes to your family’s house, and in the house there are people before whom she is not allowed to uncover, then she should remain in her hijab. There is nothing wrong with her sitting in the family gathering if it is free of the infractions referred to, namely looking, being alone together, shaking hands and speaking softly. But it is better for her to sit with the women in a separate gathering, so that she can take off her hijab and speak about anything she wants to discuss to without any problems.
With regard to what some families do of allowing women to sit with men who are non-mahrams to them, and they become too relaxed in talking, laughing, shaking hands and looking, this is haraam and those who do that have brought upon their families many negative consequences, as is well known.
We ask Allah, may He be exalted, to help and guide us and you.
And Allah knows best.