Can she go with her husband’s brother and his wife to visit a woman who is sick?

For moving about in the same city, there is no stipulation that one should be accompanied by a mahram; rather what is stipulated is that it should be safe and there should be no causes of temptation, and it is also stipulated that a man should not be alone with a woman who is not his mahram.

That “being alone” (khulwah) does not happen if there is another, trustworthy woman present.

Based on that, there is nothing wrong with going with your husband’s brother, in the company of his mother or sister or wife, to visit your relative, even if that is in the car, because there is no being alone in that case.

Al-Bukhari (1862) and Muslim (1341) narrated from Ibn ‘Abbas (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “No man should be alone with a [non-mahram] woman unless she has a mahram with her.”

An-Nawawi said:

The Prophet’s words, “unless she has a mahram with her” may be understood to mean a mahram of hers, or they may be understood to mean a mahram of hers or of his. This second interpretation is what is in accordance with the basic principles set out by the jurists, so it makes no difference whether she has with her a mahram of hers, such as her son, brother, mother or sister, or it is a mahram of his, such as his sister, daughter, paternal aunt or maternal aunt. It is permissible for the man to sit with her in such cases."(Sharh Sahih Muslim).

Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said: If there is someone who transports girls or teachers, no woman should ever travel on her own with him, because that is the khulwah (“being alone”) that is prohibited. But two women may travel with him, no problem. If someone says: Each woman will exit the bus when she reaches her house, so how can two women travel? We say: Praise be to Allah. If two women’s houses are close to one another, then let one of them come to the house of the other one, and let the two of them get into the vehicle with the driver. This applies if there is not one of the driver’s mahrams with him. If a woman who is one of his mahrams is with him, that is sufficient."(Al-Liqa’ ash-Shahri 1/58).

And Allah knows best.