I feel so sorry for all of you, you, your sister, and your tiny half sister.
It's a hell of a responsibility to take on.
I have a friend who adores kids. So much so, she has several of her own, but when the last one went to school, she and her DH decided to long-term foster. They were offered a beautiful little baby, who, coincidentally, another friend of mine had had from birth as a short term foster carer.
The birth mother had Issues - MH, her own mother had been a substance abuser, and so was she. Baby was born addicted.
Child is now 2.5 and is an absolute disaster zone. Can't help it - child is being assessed for all sorts of issues, some related to substance abuse in utero, others related to neurodiversity (possibly because of substance abuse, possibly inherited). This child now completely dictates everything that happens in that household, and my friend, who is utterly lovely, is almost at the end of her tether. She has been so close recently to taking the child back and saying "I just can't do this any more".
Long term fostering in Australia is almost as good as adoption (very difficult to adopt here because of history) so this would be a pretty major step, and it shows the extremes to which this child has driven them that she would even consider that.
Friend's next youngest children are all at school so get respite then - but when they're home, they hide in their rooms to stay safe from the foster child.
Child is still loved and cared for, very well, but they're finding it very challenging indeed. Even people the child likes get attacked and bitten, pinched, scratched - my DS2 has, and so have I.
They're hoping desperately to get any level of diagnosis in place so that they can start accessing specialist help for this child - they still love the child and want to do their best for the child but without destroying the rest of the family.
I think if you can do shared care with your sister, it would be one way to reduce the effects on your own children - and your little sister would feel that she had more family to love and care for her.