I read this as "Your books are at her place" is this wrong?
"Nála" just means something like "at her" or "with her" so not necessarily at her place.
It is very similar to the russian construction:
У нее (есть) твои книги
at her / by her (are) your books
= she has your books
Well, there is a little difference, maybe not sooo important.
But the version with "neki van(nak)" is a more general statement, while "nála van(nak)" says, that she has the object(s) with her now: in her hands, in her bag and so on.
Maybe you have in Russian that little difference as well? When I learnt Russian in school I only learnt the version you explained above - with the difficulty, that a negation needs the Genitive ;-)
Согласен. И возможно нам даже легче было бы учить венгерский с русского а не с английского..
It is correct, I would say a bit correcter than Duolingos version, because "nála" means "with her", "by her" in that context.
"She has your books." I would rather translate this way:
Neki vannak a te könyveid. / Neki vannak a könyveid. / A könyveid neki vannak. / A te könyveid neki vannak.