It can be very hard to say which particular moves are better or worse within a political system as screwed up as this one is. Ideally, there would be no public schools, no taxes, no guys with guns taking kids away from their parents if they didn't send them to school, and so on. As always, it's impossible to predict the spontaneous order that would result from the free actions of millions of individuals, so I won't even try to describe my own imaginings of what might come to be. Let's just assume that parents would choose the education they thought best for their children (or children would choose...) within the means of their unexploited income. They would obviously choose to educate their children according to what they believe is true: their own worldview and their own values. To do otherwise is insane (unless you're living under a regime so oppressive that it will kill you if you express unapproved beliefs).
Some people have world views that are based - however imperfectly - on scientific thinking: i.e., reasoning logically from the available evidence. Others believe in other epistemological methods in addition to that, such as faith and divine revelation. Many have secular moral views that are held with as much religious fervor and as little evidential grounding as those of religious people. But none of us perceives the world perfectly, and the best we can do for our children and students is to teach them what we believe to be true, and how we believe truth is acquired.
When people start picking up guns (making laws) to force their own world views on others or on others' children, oppression and strife results. I think this is the inevitable result of a national, tax-funded, mandatory educational system. People are forced to fund it, children are forced to go there, and bitter strife over what should be taught follows as inevitably as night follows day. The strife over how all our children should be educated results from the nationalistic assumption that all children living under the control of a specific "government" within some political boundary can and should be educated the same way. Everyone has ideas about it, and everyone believes that their ideas should be forced on everyone else.
A vague question like: should we put God back into schools? entails so many undefined assumptions that it really can't be answered. Distinctions must be made between schools that are freely chosen and those that are forced on people. Also, "God" certainly must be defined if the question is to be answered.
I bring whatever divinity I possess wherever I go. I try to bring love, and a profound respect for the humanity of others wherever I go. I try to seek the truth with an open mind. I would say that if you think God needs to be in a school or anywhere else, you must take him (or it) there yourself: you must take your own conception of him (or it) inside of yourself. Don't try to make laws about it. Leave others in freedom to pray or not pray to whomever they please. Leave others in freedom to seek truth the way they think best, and to speak what they believe to be true. Beliefs, values, and world views cannot be changed by force. But if you live your own conception of God, others may be drawn to that conception.
Of course, these are just my ideas, based on my values ...