Is it permissible for a husband to ask his wife to leave a communication group that includes her sisters, fearing that their husbands might see what the women exchange?

A woman must observe hijab in front of her sister's husband, because he is not a mahram to her, and being lenient in this matter is forbidden. The Prophet (peace be upon him) warned against entering upon women and explained that "the hamw is death." The hamw here refers to the husband's non-mahram relatives, such as his brother, paternal uncle, and son. Being alone with them is more dangerous than with a stranger because people tend to be lenient in such situations.

Anything that leads to fitna (temptation/strife) must have its door closed. Therefore, the husband must instruct his wife to cease communication with her sisters in a manner that exposes her to her sister's husband, and to suffice with secure communication. This falls under the Almighty's saying: ﴿O YOU WHO HAVE BELIEVED, PROTECT YOURSELVES AND YOUR FAMILIES FROM A FIRE﴾ [At-Tahrim: 6]. The guidance should be delivered with gentleness and kindness, while ensuring that ties of kinship are not severed.

As for voice communication that does not involve video or pictures, it is an easy matter, even if the sister's husband answers for a reason, as long as it is not habitual, and without a soft voice or suspicion. The sisters should be alerted to the necessity of the sister herself answering, or leaving the call unanswered until the sister is able to respond.