In what order should I play the DLC, in cohesion with the main story?
If you want a specific order to follow, you could go by the order each DLC area was released:
- Crown of the Sunken King (July 22nd)
- Crown of the Old Iron King (August 26th)
- Crown of the Ivory King (September 30th)
There's also the order that each becomes available as you play through the game (assuming you clear the Old Iron King's path before going towards the Rotten):
- Old Iron King (The Heavy Iron Key is located in the Forest of Fallen Giants, locked in an area that requires a key found in the Iron Keep after turning off the flames)
- Crown of the Sunken King (The Dragon Talon can be found behind a door down the large hole in Majula after acquiring a key from Black Gulch)
- Crown of the Ivory King (The Frozen Flower is found near the first bonfire in Drangleic Castle)
But in terms of difficulty, they're all challenging and intended to be played late enough in the game (after you've talked to Vendrick) that there shouldn't be too much of a level-difference between your character before/after each DLC area.