I could well see me being the sister OP is angry at in this scenario. I have no kids mainly because I knew I didn't have the temperament or patience for it, I need a lot of peace and quiet and order to maintain my mental equilibrium and those things obviously don't sit well with being a parent!
For the record, I'm not a child hater, I enjoy seeing my friends' children and am kind to children in public places etc.
I have a teenage niece I haven't seen since she was about 4 (my family is quite fragmented and dysfunctional and we all live hundreds of miles from each other), and a 5 year old nephew I've never met. Other than DNA, I have zero connection to either of them, and I don't love them because I don't know them. It would be like asking me to take on some random child off the street.
Because of the ages and home setups of other people in the family, I'm pretty sure I'd be seen as the 'best' option, particularly for the 5 year old (who is ND with challenging behaviour). Whilst practically I might look like the best solution (no other kids, space, money etc), emotionally I'd probably be the worst and I can't foresee any other outcome than me hating every minute of it, potentially losing my (full on, demanding) career and my marriage in the process. I wouldn't be willing to do that for a child I barely know. If that makes me a monster so be it. I would be happy to advocate and support, and do sleepovers etc, but not to have them live with me.
I'd be interested to know what kind of relationship the sister that OP is criticising had with the 14 yo prior to her going to live with her. I suspect if I had a close loving regular relationship with my niblings (or even knew them!) I might feel differently about it, it's difficult to say.