I expect this isn't to do with money, but with attention. Your niece (quite rightly) feels that she worked very hard, caused no trouble, had a rotten time and was ignored and not helped to get out of the situation she is in.
We have treated our children differently - spent much more money on one than the others, and let one have much more attention than the others. But that was by necessity, and we have spent a lot of time discussing the situation with them individually in the hope that they will understand.
Instead of saying to your niece "we have done this, tough, nothing to do with you", they should be saying "it's only now that we realise how hard you had it, we know now we should have done things differently, it's a great credit to you that you did so well with such a bad start and we really, really appreciate how hard you worked to get where you are. We appreciate that your brother won't do that, so we are doing for him what we should have, with hindsight, done for you".
They need to listen to listen to her and actually hear her -this isn't about money, it's about the fact that she feels they care more for her brother. And (unless they are happy for her to believe it) it is up to then to persuade her otherwise.
I don't, by the way, think this is either intentionally sexist or intentional favouristm - there are many things I do differently with ds2 because I have learned from ds1. That doesn't mean I love him more, it just means that with greater experience of parenting, I see the warning signals and am able to react more quickly.
Your SIL may be realising what will happen if they send a lazy and possibly not very well behaved 11 year old to an appalling state comp
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If you niece can be persuaded to look at this from her brother's point of view, she might realise that her parents are actually doing the right thing - but they also owe her an apology and an explanation.