I can't help but feel, first off,: whether Husky or not, this is a dog with a strong bond to you,you; and really, you and your family and pets are her pack. I'm tempted to add, what else seems obvious. (And with the backgrundbackground story, you're probably her true and only Alpha.) Further seeming obvious, and so it feels, to this dog your brother isn't even part of her pack as she's not acting comfortable when she is with him.
This is painful but it feels so illogical to me to even expect that she would see herself as your brother's dog. From what you are telling us, this dog is rather apparently neither sharing nor enjoying life with your brother when she is made to be with him. I'm very sorry, but from everything you write, it feels so illogical to me how your brother could even be said to "have" this dog. How do you have a dog when that's supposed to mean you are with the dog every other weekend and that's not where that dog is at home, i.e where she spends all her time. It feels more natural to me to think that she really belongs to you.