Interesting discussion. I think the most important point made by PPs is the one about her genuine feeling, rather than just intellectually understanding, that this decision is made for her benefit and not for yours or her brother's. I think in practice, this is really difficult to achieve with a child who's been a young carer all their life. These children almost inevitably have to sublimate their needs and wants to their sibling a bit more than other children do, however hard we try, as parents, to prevent that. Honestly I would try to get some advice from a young carers' charity or similar.
I'm no fan of boarding. I also think the damage it can cause tends to hit quite late in life. At 18 or even 25 I'd have said it was "fine" and I "thrived", just like parents of current or recent boarders tend to do. Having my own children made me increasingly uncomfortable with it, but it hit me like bulldozer when my own children turned the age I'd been when I started boarding. Proper breakdown stuff. My mother maintains it was what I chose, so it wasn't on her head. I feel that is way too much to put on a child that age. The buck stops with you, not her, if she does end up feeling like she's been pushed out of the family.
Thinking about my own experience, as a boarder with a day schooled sibling, and knowing my NT 12 year old who has an autistic sibling, I don't think I could be confident enough that we could really ensure she did still feel as wanted and loved as her brother. (Sorry for the insanely long sentence.) I'm sure others will disagree. My parents, as parents of a day child and a boarder, for a start.
Another caveat I'd add is that it's easy for us to say she can always change schools, but that can feel like an utterly terrifying leap to a 13 or 14 year old. At that age it's all about fitting in. Moving from a boarding school to a day school is that much more of a leap than moving even from private into state or vice versa, because it affects the "culture" and structure of your whole world. As adults we can see the bigger picture and I think it's very easy for us to underestimate how hard a leap that could seem to her. I'd worry that she'd be likely to stick with the devil she knew, even if she were unhappy.
There are no easy answers. I think it partly depends on your home and how well you can meet her needs at home, keep them apart etc, with her brother there.