The Constitution does not reference the Christian god, nor is this country founded on the ideology of Christianity, nor were all the founders adamant on pushing Christianity into the government. This is all blatantly obvious with just a little research and just a little reading into the context of the foundation.
"In God We Trust" and the "under God" (in the Pledge) were both added in the midst of the Cold War to nonsensically combat the view of "evil, godless communism." They are not an accurate representation of the American public, and they are blatantly unconstitutional additions which should be done away with.
The teaching of theistic beliefs has no place in public schools. If you want to teach the history of religions, the cultural/political ties religions have, and other topics like that that, go ahead. But the actual teaching children to have faith in any specific god(s) or follow a certain religion is absolutely unacceptable in public education. It is, frankly, morally reprehensible to teach younger children those things...along with it being obviously unconstitutional by the terms of the Establishment Clause.
Contrary to silly popular belief, barring of religious teaching from public schools was not put in place to remove people's rights, it is there to protect rights. If a school board all the sudden decided they wanted to start teaching Islam in a school district, began holding specific prayer times throughout the school day to pray to Allah, began mandatory teaching of Islamic traditions and beliefs, etc. people (Christians specifically) would be in uproar. With the structure that is currently in place, this could never happen legally -- there is no legal basis for the teaching of any religious beliefs in public schools. If you don't like it, get the Constitution amended; if you do so, I think you'll find that your rights are going to be infringed upon quite often and nobody will be there to stop it.
There is a place for education and there is a place for religion. Education is meant for schools, religion is meant for churches (or private schools).
god is a good thing, without him the world would be in constant chaos. maybe if god was allowed in schools there wouldn't be so much violence and bullying. 
No, really there would likely be less chaos and more agreement.
There is no logical basis for saying there would be less violence/bullying if religion were pushed harder in schools.