First off, I understand your neighbor wanting to protect her grandchild but just pitching all the cats outside and then slacking off on their care, make my blood boil.I am glad that the baby is doing fine, sounds like the poor little tyke had a really rough start, but she can't be that big of an animal lover if she did that.
I don't know what to tell you Yes or No. I can't understand how you do it with your 9!!! I struggle with 1 dog and 1 cat and would love to add 1 more of each!!! So I can't help you there. Could you foster this lovely cat until you find her a home?

Good Luck!