"Where is her child?"
Translation:Где её ребёнок?
You're asking why ребёночк isn't cast in accusative (animate) case (which takes on the same ending as the genitive case) because "child" seems to be the direct object of "where is" and thus should be in accusative case.
I have not seen any explanation to that question here, but I believe it is because "child" is a predicate nominative and not a direct object - it operates to name or qualify or further define the subject, and is in nominative case.
We see that operating often in English - "Where am I", not "Where am me".
One of the most common errors of colloquial English is the phrase "It's me". The grammatically correct phrasing should always be "It is I", because "I" is in nominative case - it's a predicate nominative of the subject "It" - but if you use the "correct" English, you sound extremely formal - or like you're auditioning for a play by a 19th century playwright.
Неё is used after prepositions, e.g. «у нее́».
(Except when it's a part of a phrase and modifies other word, e.g. «у её ребёнка».)