I don't really think that you need to justify asking your SD to babysit Fiona - it's what families do. They help each other out and contibute to the household in whatever way is most appropriate.
I think that it sucks that your friend asked your SD to babysit even after hearing that she let you down. I expect my friends to back up my parenting choices - if they disagree they can talk about it with me while the children are out of earshot but in the meantime they can just refrain from undermining me.