“The church is supposed to direct the Government, the government is not supposed to direct the church”.
That is 100% correct.
It actually is, since members of the Church in the United States are the American people, and ours is a government of, for, and by the people, it's the Church (Americans who are members of churches, either individually, or acting as churches) who are supposed to direct government. As for statement number two, this is clear by a simple reading of the First Amendment.