He does not allow his wife to appear in front of his brothers
A woman has to cover her entire body, including the face, from men who are strangers to her (i.e., non-mahrams). She should observe hijab even more strictly in front of her husband’s male relatives who are not mahrams for her than in front of strangers. This is the opposite of what most careless people do nowadays. The Prophet (peace and blessings of Allaah be upon him) said, when one of his companions wanted an exception to allow the husband’s relatives to enter upon his wife: “The in-law is death.” So we must be more cautious with regard to the husband’s relatives – including his brothers – because of the carelessness that exists with regard to this matter.
Your brother has done well by not allowing his wife to appear in front of you, and she has done well by obeying the command of Allaah and of her husband. This is not extremism at all; rather it is obedience to the command of Allaah. There is no need for the husband’s brothers to see his wife, let alone sit with her and talk to her.
Those scholars who said it is permissible for a woman to sit with her husband’s relatives only allowed it on condition that there is no suspicion attached to that and that she does not sit alone with one of them, or there is no listening to songs or watching haraam things on the part of either of them. Unfortunately such things happen in most people’s gatherings. If the gathering is free of the above-mentioned evils and haraam things and the woman observes full hijab, then it is permissible for her to sit with them and speak to them, so long as she is not soft in speech. But it is still better and more on the safe side for her not to do that, and this is what your brother has done, so that hearts may remain pure and free of the traps by which the Shaytaan ensnares people.
What your brother has done should not have any effect on your relationship with him or on the relationship of your wives with his wife. They are doing something good and acting in accordance with Islam. You should try to get close to them and learn from them in the way they deal with people. You should note that your brothers’ criticizing their brother for concealing his wife from them and not letting her sit with them makes one have suspicions about them. In sha Allaah they are not that type of people, but the Shaytaan may make something appear attractive to a man so that what is good becomes bad to him, and what is bad becomes good, so he regards covering and modesty as extremism and laxity as trust and progress.
We ask Allaah to purify our hearts and bodies, and to bring you together in a good way, and to reconcile between you, and to make you a good example to other people.
See also the answers to questions no. 21363 and 13261
And Allaah knows best.