A basic belief of the most extreme elements of the Christian Right, and one which is gaining traction in the rest of the movement, is the idea that God has given Dominion over the planet generally and America in particular to Christians. This is as much a political as a theological doctrine and leads such Christians to the belief that they have been authorized by God to assume political control of the United States.
They mean to ensure that America is a "Christian Nation" in every sense of the word -- historically, culturally, legally, and politically. Whereas the language of theocracy often seems to be more a rhetorical strategy for many on the Christian right, for Dominionists it's a deliberate expression of a conscious agenda. It is for this reason that they can accurately be labeled "Christian Nationalists," for they are Christians who seek to transform America into a nation defined exclusively along the doctrinal and theological lines of their brand of Christianity.
An important component of this agenda naturally lies in the education of young people. Public schools are under constant attack for being secular, for not promoting Christianity, for having classes dealing with sexuality or evolution, and so forth. In their place, conservative evangelicals are promoting special Christian schools where ideology trumps education and reality. These schools may teach creationism over evolution, a warped view of history (especially American history), and worse.
The above image was originally taken from a World War II poster which said "This is America... ...where every boy can dream of being President. Where free schools, free opportunity, free enterprise, have built the most decent nation on earth. A nation built upon the rights of all men. This is your America ...Keep it Free!" This sentiment is much the opposite of the Christian Nationalists who don't want to see anyone by Christians hold elected offices, who want to see an end to free public schools, and who don't really believe in any "rights" not constrained by Christian doctrines.