I'd say no. Difficult terrain makes all movement cost double. So to move 5 feet, you have to use up 10 feet of movement. Dodging Panache only grants 5 feet for moving, so you cannot use it just as you can't use a 5' step to move in difficult terrain.
I second a no. You need 10' of movement to move 5' in difficult terrain.
If you had nimble steps though, that would solve it.
Because it requires 10ft of movement to move into the square and you only have 5ft granted by Dodging Panache.
I see your point Murphys.. however here are my thoughts.
There are basically two methods of 'movement' in pathfinder
A move action or a 5' step. Since this is not a 5' step, it should be the equivalent of a 5' move action. A move action of 5' without a movement cost.
Since you can spent a move action to move through difficult terrain, albet at 2x the movement cost, you should be able to take this 5' movement in difficult terrain, specifically because it does not have a movement cost and BECAUSE it's a move action, it invokes an the AOO.
Where is my logic wrong there?
You get to move 5'.
In difficult terrain, it takes 10' to move 5'.
The effect does not say you get to ignore difficult terrain, so you don't.
Therefore, your 5' of movement distance the effect grants is not enough to move a 5' square in difficult terrain because you need to be able to move 10' to do so.