This sentence doesn't make sense to me - if the plural of children is used then should the plural "their books" also be used?
No, 'haar' does not refer to 'de kinderen', nor 'boeken'. It refers to a third party, a woman/girl (could be the writer, but it could also be a woman that owns the books that those children are reading).
Oh thanks so much for the explanation - that makes sense - I didn't think of that meaning!!
Onze is for de words and ons is for het words, so de kinderen = onze kinderen.
Curiously, this sentence is (as far as I can tell) ambiguous in precisely the same way as its English translation, which is rare across languages.
If talking about a man, we'd say:
Onze kinderen lezen zijn boeken. -- "Our children read his books.*
Onze kinderen lezen hem boeken. -- "Our children read him books.*
In the feminine, in both languages, the possessive-dative distinction is lost.
"onze kinderen lezen hem boeken" is certainly not wrong, but it won't be something I would say as a native speaker. In this case I would use the verb "voorlezen": "Onze kinderen lezen hem boeken voor"
So if the book belongs to a guy, will it be "onze kinderen lezen hij boeken"!?