Is it considered a sin to cut ties with one's wife's sister due to her careless actions, treating one as a servant, and not appreciating the hospitality extended to her?

What your husband's sister does by visiting without permission is not permissible, for homes have their sanctity and entry is not allowed except after seeking permission, as Allah Almighty says: "O you who have believed, do not enter houses other than your own houses until you ask permission and greet their people. That is better for you that you may be reminded." You should be patient with her and forgive her, and ask your husband to advise her regarding the Shari'ah ruling on seeking permission. If she insists, then your husband must prevent her from doing what causes you harm. You are not obligated to serve her or her husband, and it is not permissible for you to appear before her husband without the legal hijab.