Yes, but it is saying that there are, in fact, multiple children that could be hers. It's not focusing on which one IS hers, it is focusing on the fact that anyone of those children could be hers.
And yes, I do upvote my own posts because you are supposed to upvote posts you agree with. On Reddit, as soon as you post something, it automatically upvotes it because you wouldn't post something you don't agree with. I agree with what I'm saying because it is true.
No, it says that one of her children is hers. The subject of the sentence is the word one, not the word children. Try to make a syntax tree. In Czech you see it nicely with dětí in genitive but in English it is pretty much the same thing.
It looks weird to me, but possible here. Your choice...