Am I sinful for what happened between me and my husband's sisters—the quarrel, the hitting, and the accusations? And am I sinful for cutting ties if being close to them causes me problems that could lead to divorce?

You bear no sin for what happened with your relatives, and refraining from responding to their transgression is more befitting. There is no harm in severing ties with these relatives as long as maintaining the relationship brings harm. The prohibition of severing ties applies to unmarriageable kin (dhul-rahim al-muharram) such as brothers and sisters, while it is disliked to sever ties with marriageable kin (dhul-rahim ghayr al-muharram) such as paternal and maternal cousins.