Re: Hurt by SIL’s opinion of me 
Is that all she said, just the one liner? If yes, then isn’t this a typical case of making a mountain of a mere mole hole? I mean, it isn’t really much to begin with. She simply agreed with him, the other option may well have been to disagree and come out as the rude one.
Maybe she cares less about what he actually thinks of her bhabhi?. Additionally and from the little I’ve understood, she’s always treated you as nice as any bhabhi would ever expect from their SIL.
In the end, it shouldn’t take this less (a single liner) to bring down a perfect working relationship of a bhabhi and her nand.