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.