Unity 2d object advanced rotation

Your question looks extremely similar to this one: https://answers.unity.com/questions/1685799/how-to-rotate-a-line-by-its-other-end.html

I've taken that code and modified it to actually rotate a sprite instead of just drawing a line with a lineRenderer. You can take out the line renderer code if you want, but it will make it easy for you to see what's going on. Don't forget to set spriteLength to the actual length of your sprite. Most of the changes I made I just tacked on to the end of SetLinePoints()

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 public class DisRotTest : MonoBehaviour
 {
 
     public Transform point1, point2;
     public Transform sprite; 
     
     public Camera cam;
     public float spriteLength = 10;
 
     private LineRenderer lr;
     private Transform grabbedPoint, stationaryPoint;
     private Vector3[] lrPoints;
     private Vector3 offset;
     void Start()
     {
         //Set the initial line length to 10
         point2.position = point1.position + spriteLength * Vector3.right;
 
         //I'm using a line renderer to draw the line
         lr = GetComponent<LineRenderer>();
         lrPoints = new Vector3[2];
 
         //Tell the line renderer to update its points
         SetLinePoints();
 
         grabbedPoint = stationaryPoint = null;
     }
 
     private void Update()
     {
         //Grab mouse position every frame
         Vector3 mousePos = cam.ScreenToWorldPoint(Input.mousePosition);
 
         //I want to rotate on the X-Y plane, so I'm going to align the mousePosition with my gameObject on the Z axis
         mousePos.z = transform.position.z;
 
         //When we click, grab the closest point
         if (Input.GetMouseButtonDown(0))
         {
             grabbedPoint = Vector3.Distance(mousePos, point1.position) < Vector3.Distance(mousePos, point2.position) ? point1 : point2;
             stationaryPoint = grabbedPoint == point1 ? point2 : point1;
         }
 
         //While we drag, make the line go through our mouse position
         if (Input.GetMouseButton(0))
         {
             offset = mousePos - stationaryPoint.position;
             offset = offset.normalized * spriteLength; //Set line length to 10
             grabbedPoint.position = stationaryPoint.position + offset;
         }
         //Tell the line renderer to update
         SetLinePoints();
     }
 
     private void SetLinePoints()
     {
         lrPoints[0] = point1.position;
         lrPoints[1] = point2.position;
         lr.SetPositions(lrPoints);
 
         //Move sprite to the right of point1 and reset its rotation
         sprite.transform.position = point1.position + new Vector3(spriteLength/2f, 0,0);
         sprite.rotation = Quaternion.identity;
 
         //May have to flip some things based on rotation and which point we grabbed
         float isNegative = offset.y < 0 ? -1 : 1;
         float negativeOffset = stationaryPoint == point1 ? 1 : -1;
 
         //Rotate sprite AROUND point1 by the vector angle between point 1 and point 2
         sprite.RotateAround(point1.position, Vector3.forward, negativeOffset*isNegative*Vector3.Angle(Vector3.right, negativeOffset*offset));
     }
 }
 

Let me know if this works for you