I can't help but feel, first off: whether Husky or not, this is a dog with a strong bond to you; and really, you and your family and pets are her pack. I'm tempted to add, what else seems obvious. (And with the background 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.
Going from that, when your brother "picks her up", it seems, to her it just means that she is being taken away from her pack, which is where she belongs, where she is at home, and where she feels safe. Being taken away from home. And away from all the fun, too. Her behavior as you describe it seems very congruent with a strongly grieving, worried or offended dog. Grieving or worried, more like (she might eat if just offended, unless she also just refused to accept something from him, too.)
Now for the Husky part, I've never raised a litter of Huskies or owned one, but as the saying goes that Huskies are a breed in the range of the closest you can get to a wolf, the pack idea would surely apply even more, and strongly. And the idea of not accepting food from him under these circumstances, too.
One thing you didn't ask, and a potentially painful one - but I can't avoid the subject without feeling untrue (and I've already touched it anyway) - you may want to keep in mind that a dog's native language in every respect (perception, emotion, expression and so on) is well, Dog, not Human. This includes that what counts is what really happens. The being together, the even having been mostly brought up by you, the sharing of most all of her life. The human concept of isolated juridical ownership is not included in what's real or comprehensible to a dog.
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.
When I was first going to write, "This dog's behavior when she is with your brother, ...", I had to physically restrain myself from not starting that paragraph with Your dog. As that is by all means in what I can see from your post, where she is bonded, so, where she belongs.
And I guess she is expressing that strongly. Which of course raises a completely different question that you didn't ask, but that's all I can see here, and so sorry, I can't hold this back.
(And I think she doesn't. What appears to you to be jealousy may just be putting much energy and vigilance into not being separated from you yet again.)
Coming back to your original question, what I think I observed from your post might be gradually different with a breed that mingles easily with just anyone (being very far from having retained a strong inner concept of pack), but then, how little of a dog must a dog have become for that? To the extent of things you describe, I wouldn't even know for sure whether such a breed even exists. Some breeds would sure mingle more easily than others, but then, that's not the same as being inconsistent as to where is home. And my take of this is, as for Husky specific, inconsistency in that quarter would surely go the least with a close-to-wolf breed dog.
