Thank you Perikles for that corrections. I'll bear in mind what you say about articles.
About the other phrase. What I wanted to say was: "Si toda la educación de los niños depende (o se basa) en sus padres..." As Angelica points.
Anyway, I will stay with: "If children have to rely exclusively on their parents for their education"
I understand that is very important to be clear about which is the subject to avoid errors!
