How to work out the rotation of a pivot to point an offset vector at a target?

Title is confusing and I am bad with words.

In your typical 2D game, to aim a gun at something, you might work out the angle between the pivot and the target and simply rotate.

However, my guy doesn't hold the gun directly along the pivot. See the following gif for what happens if I try that method:

http://i.imgur.com/hU7nVJD.gif

What I really want, is the red line to always point at the mouse, not the white line.

I've tried the following script:

 using UnityEngine;
 using System.Collections;
 
 public class RotateOffset : MonoBehaviour
 {
 
     [SerializeField]
     Transform _source;
     [SerializeField]
     Transform _directionSource;
     [SerializeField]
     Transform _pivot;
 
     // Update is called once per frame
     void Update()
     {
         Vector3 mousePosition = Camera.main.ScreenToWorldPoint(Input.mousePosition);
 
 
         Vector2 mousePos = new Vector2(mousePosition.x, mousePosition.y);
         Vector2 pivotPos = new Vector2(_pivot.position.x, _pivot.position.y);
         Vector2 sourcePos = new Vector2(_source.position.x, _source.position.y);
         Vector2 directionSourcePos = new Vector2(_directionSource.position.x, _directionSource.position.y);
         // wasn't sure how to work out a relative direction, so had to use tranforms
         Vector2 direction = directionSourcePos - sourcePos;
 
         // attempting basic trig (which I'm not very good at)
 
         // from pivot to source is one side
         float sideB = Vector2.Distance(pivotPos, sourcePos);
         // this angle is fixed given the pivot -> source -> direction relationship
         float angleB = Vector2.Angle(pivotPos - sourcePos, direction);
         // from pivot to mouse is another side
         float sideA = Vector2.Distance(mousePos, pivotPos);
 
         // So I actually want AngleC here, meaning i have to work out AngleA first as I don't know C or AngleC
 
         // sine rule
         float sinB = Mathf.Sin(angleB * Mathf.Deg2Rad);
         sinB = sinB / sideB; // had to split these steps out for some reason - was giving the same answer no matter the input if done on one line?
         sinB = sinB * sideA;
         float angleA = Mathf.Asin(sinB) * Mathf.Rad2Deg;
 
         // can now get AngleC with the fact triangles add up to 180
         float angleC = 180f - angleB - angleA;
 
         // I originally tried to just set the pivot rotation here but it didn't work
         // _pivot.transform.eulerAngles = new Vector3(0, 0, angleC);
 
         // so I tried to attempt to work out some kind of offset to work out where that angle exists in world space
         // translate target back to origin and atan2 magic it
         float offset = Mathf.Atan2(mousePos.x - pivotPos.x, mousePos.y - pivotPos.y);
         // use the angleC with the offset... I've tried angle - offset, offset - angle, angle + offset
         _pivot.transform.eulerAngles = new Vector3(0, 0, angleC - offset);
 
     }
 }
 

But it doesn't quite work. I think I've got confused somewhere.

I've made sure to test this with just positive X and Y values, in case going over an axis confuses it. It doesn't work in any of the 4 'areas' around the pivot (i.e. X, Y, -X, -Y relative to pivot).