Something that you're totally not adding into this mix is that you are just a few years out of this situation yourself, and you are vaulting up to the plate to take on something that will be totally life changing and a huge job for you personally. Okay, are you married? What does your spouse think about what you are wanting to do? Do you have a huge income? Do you own your own home, or have a place big enough that the landlord would be open to two more residents? Do you have lots of well thought out plans for arranging the care of your somewhat disabled sibling, possibly for over the long haul? How is all this going to affect your work life? Your home life ? What about the person you're in a relationship with, if you are? Do you have children of your own? Where are they in this situation?
What are you going to do if you get these two nearly grown individuals there with you, whatever your current living and relationship situation is, and they suddenly announce, "You're not the boss of me!" and start doing something really bad, or simply leave? Any family court is going to look at a lot of things other than just the unfitness of their current situation based on a lot of your stories about the past and guesses about what's going on now. One of those things is if where they'd be after this requested change an appropriate placement for them.
And it's likely that any disabled person such as you describe your brother to be comes with a certain amount of state support, which will make his current placement site hang on like bloody murder, regardless of what she may be saying. She's living to some extent, off that money. To be cold, your brother has value as an income source, That will be considered strongly by any court determining his placement.
I understand how you feel. When one older sibling gets out of a very dysfunctional childhood situation, the fantasy they tend to have is that they'll come back and somehow make it better for their younger siblings, save them from all that misery. But you really need to go about this carefully and thoughtfully, and with the advice of a good family attorney. If you can't afford that, you must progress even more slowly. Let me give you a huge hint. If the situation stinks, but isn't bad enough you could deal with the idea of their being removed and put in a foster care placement for a while, it likely isn't bad enough that you're going to get custody.