Husband not defending me from his sister ?

I am from the U.S., while my husband and his sister are from India. Since my husband didn’t have any family here, I was excited to sponsor his sister and help bring her to the U.S. However, from the very first day she arrived, she started making snarky comments about me. At first, I ignored them because I didn’t want any problems, but over time, the comments became more frequent and more hurtful. Instead of addressing them, my husband would direct the blame toward me, insisting that I was in the wrong and never questioning his sister’s behavior. One particular incident that stood out was when she got upset because I couldn’t take her to do her laundry. I had just given birth to a newborn, and she lived an hour away from me. Rather than understanding my situation, she started complaining to my husband, which led to him arguing with me instead of supporting me. Another issue arose when I asked her to contribute $50 toward her phone bill, which also became a problem. Despite all of this, when she broke her foot, I took care of all her doctor’s appointments and made sure she received the proper treatment. But instead of appreciating my efforts, she became even ruder toward me. I don’t understand what I’ve done wrong, and the worst part is that my husband refuses to defend me. He claims that he can’t speak to his sister directly because it’s a “cultural thing,” but I honestly think that’s just an excuse. We’ve argued about this issue more than a dozen times, yet nothing ever changes. Is this truly a cultural issue, or is my husband just afraid to stand up to his sister?