Is the husband considered sinful for severing ties of kinship with his sister, who caused family problems that escalated to her insulting the wife and inciting her parents against them, with the parents believing the sister, while the husband continues to honor his parents and maintain ties with his other siblings? Is the sister considered a kin relation to the wife, and is it permissible for the wife to distance herself from her and from the husband's parents to avoid fitna (strife/temptation)?

The questioner did well in initiating reconciliation. Avoiding the husband's sister and parents might be the best solution if maintaining the connection causes problems, especially if matters reach the point of slandering reputations. This is because the husband's family are not uterine relatives (arham) whose connection is obligatory upon you, but rather upon the husband.

He must endure their harm and strive to maintain ties with them in a way that does not increase problems. He should treat his sister with gentleness and good manners, and his parents with kindness. You should help him in this and remind him of Allah's saying: (And not equal are the good deed and the bad. Repel [evil] with that which is better...) Fussilat/34.

Let your intention for keeping a distance be to await a time when hearts are clear, so that good relations can return. For Islamic law came to achieve love among people and warned against enmity, hatred, and abandonment. A Muslim should strive to reconcile disputes if animosity occurs.