Your hero should be the Suleiman the magnificent, NOT a secular Ataturk. Its a defeatist mentality to worship those who were hanging by straws as oppose to those who brought the glory in real terms. The two men were poles apart, Islamist Vs secularist. Sorry to burst your bubble but from outside, the impression of Ataturk is of some one who made his country a sidekick of western civilization, far from being a pain the backside. Having said that, todays Turkey under current leadership is moving in right direction. That why its heartening to see that Turks have resisted this secular coup with full force.
Reading Quran, praying 5 times are individual acts, they are not related how the state should work. That is where the Islamic socialism or as they say "Sharia" (way of life) comes into play. It is the most misunderstood concept or shall I say, a deliberate confusion created around it. The best way to understand it, its to look and study how the first state in Madina functioned.