Is a husband obligated to command his wife to cover her face in front of her sisters' husbands, knowing that they were like brothers to her and cared for her, and that this might cause familial problems?

The husbands of the wife's sisters are not among her mahrams. The wife must adhere to the full, prescribed Islamic veil (hijab) in front of them. This is the unalterable judgment of Allah. Do not pay attention to the anger of your mother, sisters, or their husbands. Kindly explain to them that this is a ruling from Allah which a Muslim has no choice but to follow. Remember the saying of the Prophet, peace and blessings be upon him: "Whoever pleases people by displeasing Allah, Allah will abandon him to the people. And whoever displeases people by pleasing Allah, Allah will suffice him against the burden of people."