Are the husband's sisters considered next of kin, making their visitation obligatory? And is refraining from visiting them—especially when they have cut ties—considered a severing of kin ties?

The kin with whom ties must be maintained are relatives from the father's side, sons and daughters, brothers and sisters, paternal uncles and aunts, maternal uncles and aunts, and their children. The husband's sisters are not among the wife's kin (Rahim), but they are kin to the husband and his children. Being kind to them helps the husband maintain ties with his kin. If there is no benefit in being kind to them, and they harm the wife, then the wife is not considered a severer of ties (Qati'at Rahim). However, she must not prevent her husband or children from maintaining ties with them; rather, she should encourage them to do so, and she will be rewarded for guiding others to good.