First it is supposed to be the three balancing each other out, along with the SENATE providing an annual budget and the House holding the purse strings. The Supreme Court is to make sure the laws passed are not against the Constitution. The President is just an administrator of the government.
The separation of church and state simply is o that we do not have a single religion in control of the government (as in Egypt, Iran, Iraq, the Kingdom of Saudi Arabia, etc.), it does not men removing signs of a religion, as in the Ten Commandments, from various government buildings, public lands, etc.
Just like in TV, if you don't like what's on, change he channel or turn it off. Do not scream that it is offending you!