First up, that is devastating news for anyone, and you have my total sympathy and all hopes your sister fully recovers.

Having been in a not entirely dissimilar position myself a few months ago, I can say that situations such as these are where BA comes into its own and the call centre staff are very understanding and helpful.

Others will have to comment on award availability as my experience was with a revenue ticket and needing to get home, with BA waiving all change fees and getting me on an essentially sold out flight without a murmur.

I was fortunate being a Gold member in that my travel history meant they could trust me enough not to require evidence of illness. As a Blue I’d have to say I would expect them to ask for a higher burden of proof. Getting a Doctor’s note from a foreign country may take longer than you ideally want, so in the circumstances you may want to bear that in mind and consider whether you can find the money for a revenue flight.

If you can do so, I think that would also put you in a much better position with talking to BA about moving any potential return day back if you feel you need more time with your family.