What is the ruling on a niqabi wife communicating with her family (brothers, grandparents, paternal uncles) via audio and video while her face is uncovered, knowing that she cannot see them except through this method, and that her refraining from doing so may lead to cutting off ties of kinship?

There is no objection to a woman communicating with her mahrams (unmarriageable kin) and other women, and them seeing her picture. It is preferable that she only show her face, as a precaution against devices being hacked. If her family becomes angry at her speaking with them while her face is uncovered, she may speak in this state.