It may be that she feels guilty herself because she was the one who prodded her brother into a relationship with you. She's likely to be going through similar self-doubt to what a BS feels: "How could I have so severely misjudged this person? What does that say about me and my own safety, if I can be so thoroughly taken in?"
I was about to say something similar. You have detailed in a previous post that you were close with her before you got involved with your BH, her brother. At some level, she probably does feel guilt and responsibility over introducing you two. This isn't an easy situation at all, I can see how it is natural for her to be defensive and protective over her brother, especially given the circumstances that if not for her prodding, you two never get together and thus her brother never gets hurt. However, I see that on her part as immature, because she doesn't seem to realize that both you and her brother are adults with agency to make decisions, both good and bad ones, and she has no influence on it. Of course, blood is always thicker than water, so as family, she is naturally going to take her brother's side and she was by his side at some of his darkest hours post DDay wherein you were of course the enemy.
However, I want to make one thing clear, you are under no obligation to like or be social with your in-laws and they with you. I've got in-laws that I will die a happy man if I never see again, because they are genuinely awful people, and my falling out with them has absolutely zero to do with infidelity and everything to do with their fundamentalist religious views. Your SiL doesn't have to like you, doesn't have like her brother being with you and she doesn't have to support you being together. I think it really does come down to her taking her brother's side, because imagine you two had the same relationship you had with her prior to your A and switch it up to where your H had an A (also, don't I recall that you mentioned your H slept with someone else, thus having his own A)...I can almost guarantee that if her brother cheated on you that she would still find a way to take her brother's side and while she may have been more sympathetic to you as her friend, it seems likely that she would've chosen him over you anyways, which again is probably to be expected.
She may never get over what you did to her brother and that is her burden to carry, not yours. Especially if you and your husband are able to build something new and great through reconciliation, it is on her to observe your actions and arrive at a peace with what has happened. As far as your reconciliation goes, I wouldn't spend another single solitary second worrying about what your SiL thinks, says or does, she isn't your spouse. Again, focus on your husband and the reconciliation and when the time is right, if anything, it should be him to correct his sister on her attitude. Remember, the only thing that you can control is your attitude and your approach towards things and how you are the new you, so don't stress about things you cannot change and your SiL's attitude towards you should be at the top of the list of things you shant worry about.
Best of luck and strength as you guys work through this journey together.