Control Ship and Gun Separately

Instead of having the turret be a child of your ship, you should have the ship be a child of your turret, and attach a kinematic rigidbody to it (the ship). Rotating the turret should be pretty straightforward now that it's the parent, but your movement code should not alter the turret's rotation. Now, in order to properly rotate the ship, you can attach this to the ship gameobject (which, again, should be a child of the turret):

 var rotationToHold:Quaternion;
 if(rigidbody.velocity.magnitude>0.1){//if we are moving
 transform.rotation=rigidbody.velocity; //make the ship's rotation face its movement
 rotationToHold=transform.rotation; //store this frame's rotation
 }
 else{
 transform.rotation=rotationToHold; //if not moving, keep the rotation we had on the last frame that we were moving
 }

Here is a visual representation:

 -Turret (moves with left analog stick, rotates with right analog stick, movement does not affect rotation)
    -ship (does not rotate based on input but based on velocity and is a child of turret)

Edit: Perhaps it is a fairly complex solution that would require you to radically change the way your objects are set up. I am also pretty sure that there is a much more simple way to do this that i am overlooking at the moment.

Edit 2: How can i be so silly, ignore the setup and use the code that i gave you for the turret, but instead of velocity you should check whether there is right thumbstick input.

 if(/*multiple Input.GetAxis checks here to see if there is right thumbstick input*/)
 rotationToHold=transform.rotation;
 else{ //if no right thumbstick input
 transform.rotation=rotationToHold;
 }

I am keeping my original answer up in case it suits you better though.