Is the sentence correct?

Yes, but it looks awkward. Of course children is already plural, so any native-speaker would understand right away. I don't think, however, that a native-speak would say or write that. I don't like to re-write sentences for ESL/EFL members, but in this case, I say that: "It is the children's wish that their parents would give them a solution to their problem."

Thanks, Setanta, for your explanation and for showing me how the sentence should be rewritten.