Is maintaining kinship ties obligatory with the sister-in-law who is immodest and not religiously or morally committed, and who has caused family problems, especially given that shunning her preserves the questioner's household and herself?

The wife of the brother is not considered a special kin ( رحم خاص ) whose ties must be maintained. Therefore, there is no sin upon one who does not maintain a special relationship with her, provided that the ties of kinship with the brother himself are preserved. It is permissible to boycott her ( هجرها ) if there is hope of achieving a benefit, such as deterring or disciplining her, or protecting oneself from being influenced by her sins. Otherwise, boycotting her is not permissible, and she has the right of a Muslim not to be boycotted for more than three (days).