Why is "Her children" wrong?
The real question is: how do you tell the difference between "her children" and "your children"???
Personal pronouns generally refer back to someone who had been mentioned earlier in the conversation.
Had you just been speaking about her? or about you? or about them?
It isn't. Please report it.
Her children should work too
Yes, it should. It's a mistake in this Pearson sentence that that alternative is not accepted. Report it if you'd like.