I've thought about this quite a bit, and (admittedly bending over backwards) can sort of see the brothers' POV. Imagine this scenario
You see your family home, and realise that it's a great development opportunity. Sold separately, the flats might together raise x, but if the whole property were sold as a development, it might raise 6x (for example).
But there's a drawback. Your sister has bought the downstairs flat from your parents, so no-one can buy the whole development opportunity without your sister selling up.
So you go to your sister and explain to her that it's a great opportunity and obviously you'll give her 50% of the sale price for the whole property.
Probably because you are blinded by greed, but it could be naiveity, you overlook the fact that your sister actually owns more than 50% of the property (because she ... I forget the deets here but she has the larger flat with the garden). You also completely fail to take into account the fact that your sister's DH is unwell, and just refuse to hear the fact that she doesn't want to move in any case.
(My business brain is telling me that if my ridiculous example was true, and the whole property really was worth 6x what the sum of the two flats was worth, some negotiation ought to go on. And so the OP ought to give a tiny bit of thought to what percentage of the sale price actually WOULD be fair. But a valid answer might still be 'I don't want to move, even for £1m')
If I were the brother and really believed the above, I would be trying to negotiate - and I don't think that would make me an awful person (although unless I was very stupid indeed, the initial offer of 50% says a lot about my shitty character).
Just wanted to look at it from another angle, really.