How to get object to follow a curved path to reach a moving destination?

(exaggerated rotations are intentional, you can disable them by editing rotation interpolation curve)_

 using System.Collections;
 using UnityEngine;
 
 public class CardsAnim : MonoBehaviour
 {
 
     [SerializeField] Transform _p0, _p1, _p2, _p3;
     [SerializeField] Transform _card;
     [SerializeField] float _duration = 2f;
     [SerializeField] AnimationCurve _translationInterpolation = new AnimationCurve(
         new Keyframe(0,0) , new Keyframe(0.03f,0.03f) , new Keyframe(0.3f,0.03f) , new Keyframe(1,1,4.3f,0)
     );
     [SerializeField] AnimationCurve _rotationInterpolation = new AnimationCurve(
         new Keyframe(0,0) , new Keyframe(0.82f,5.7f,26f,26f) , new Keyframe(1,1)
     );
 
     void OnEnable ()
     {
         StartCoroutine( AnimateCard() );
     }
 
     #if UNITY_EDITOR
     void OnDrawGizmos ()
     {
         if( _p1 ) { Gizmos.color = Color.red; Gizmos.DrawCube( _p1.position , Vector3.one*0.5f ); }
         if( _p2 ) { Gizmos.color = Color.blue; Gizmos.DrawCube( _p2.position , Vector3.one*0.5f ); }
         if( _p0 && _p1 && _p2 && _p3 )
         {
             Vector3 a = _p0.position, b = _p1.position, c = _p2.position, d = _p3.position;
             const int numSteps = 20;
             float dt = 1f / (float) numSteps;
             Gizmos.color = Color.white;
             for( int i=0 ; i<numSteps ; i++ )
                 Gizmos.DrawLine( SampleBezierCurve( i*dt , a , b , c , d ) , SampleBezierCurve( (i+1)*dt , a , b , c , d ) );
             Gizmos.color = Color.red;     Gizmos.DrawLine(a,b);
             Gizmos.color = Color.green; Gizmos.DrawLine(b,c);
             Gizmos.color = Color.blue;    Gizmos.DrawLine(c,d);
         }
     }
     #endif
 
     IEnumerator AnimateCard ()
     {
         float time = 0;
         yield return null;
         while( time<_duration )
         {
             float t = time/_duration;
             _card.position = SampleBezierCurve( _translationInterpolation.Evaluate(t) , _p0.position , _p1.position , _p2.position , _p3.position );
             _card.rotation = Quaternion.SlerpUnclamped( _p0.rotation , _p3.rotation , _rotationInterpolation.Evaluate(t) );
             
             yield return null;
             time += Time.deltaTime;
         }
         _card.position = _p3.position;
         _card.rotation = _p3.rotation;
 
         StartCoroutine( AnimateCard() );
     }
 
     static Vector3 SampleBezierCurve ( float t , Vector3 a , Vector3 b , Vector3 c , Vector3 d )
         => a*Mathf.Pow((1f-t),3) + b*(3f*t*Mathf.Pow((1f-t),2f)) + c*(3f*Mathf.Pow(t,2f)*(1f-t)) + d*Mathf.Pow(t,3f);
 
 }