How do I aim a tank turret at a point?

I have a tank model that can move and rotate freely on every axis. On top of it, there is a turret, which should only be able to rotate along the local Y axis, and a gun barrel connected to the turret which should only be able to pivot up and down. I want to be able to aim the gun at any point without violating these constraints, but nothing I've tried so far has worked. I guess I just don't understand quaternions :)

So can anyone give me any pointers on how to do this? I'm pretty lost.

Edit: Through trial and error, I got something that almost works. It works perfectly for any target that is approximately in front of the tank, but when the turret has to rotate a significant amount around the y axis, the gun no longer is at the right angle. I suspect this has something to do with gimbal lock but I'm not sure how to fix it.

Here's my code:

     void FixedUpdate() {
         Ray ray = Camera.main.ScreenPointToRay(Input.mousePosition);
         RaycastHit hit;
         if (Physics.Raycast(ray, out hit))
         {
             Debug.DrawLine(hit.point, Camera.main.transform.position, Color.red);
             Quaternion dir = Quaternion.LookRotation(gun.transform.position - hit.point, Vector3.up) * Quaternion.Euler(90, 0, 0);
             Vector3 localDir = (Quaternion.Inverse(transform.rotation) * dir).eulerAngles;
             turret.transform.localRotation = Quaternion.AngleAxis(-localDir.z, new Vector3(0, 0, 1));
             gun.transform.localRotation = Quaternion.AngleAxis(-localDir.x, Vector3.right);
             Debug.DrawLine(hit.point, gun.transform.position, Color.green);
         }
     }