Controlling two characters simultaneously on a grid

I'm trying to create a grid based puzzle game where you control two characters with one set of input, but each character is on their own little maze. So essentially you have to guide your two characters that move simultaneously through their own maze, to their goal own goal. So I've actually got a prototype of the game working, but I encountered some serious bugs so I decided to rework it and see if I can fix it piece by piece. My problem right now is that they're tiles on the floor that the characters can slide over. So if the one on the left slides over a tile it'll skip a space for example, and the one on the right will only move its normal one space.

My problem is that while the object on the left is still moving, the object on the right can move freely - which is not what I want! If either object is moving I want to make sure that neither object can accept input. I've tried a few ways, with more or less success depending, but the closest I can get is that you can only move if they're both not moving, but if you happen to press an input just as the sliding block reaches the end then the other block goes off sync... Does anyone know how I can do this?

I have this script on both the moving objects, and it moves nicely and slides, but it just needs to be limited:

     [Header("Test Variables")]
 public float moveSpeed1 = 4f;
 public Transform movePoint1;
 public LayerMask whatStopsMovement1;

 public static bool isSliding = false;
 public LayerMask slidingBlocks;

 // Start is called before the first frame update
 void Start()
 {
     movePoint1.parent = null;
 }

 // Update is called once per frame
 void Update()
 {

     transform.position = Vector3.MoveTowards(transform.position, movePoint1.position, moveSpeed1 * Time.deltaTime);

     if (Vector3.Distance(transform.position, movePoint1.position) == 0f)
     {
         Movement();
     }
 }

 public void Movement()
 {
     if (Input.GetKeyDown(KeyCode.LeftArrow) || Input.GetKeyDown(KeyCode.RightArrow))
     {
         if (Input.GetKeyDown(KeyCode.LeftArrow))
         {
             MovementHorizontal(-1f);
         }

         if (Input.GetKeyDown(KeyCode.RightArrow))
         {
             MovementHorizontal(1f);
         }
     }
     else if (Input.GetKeyDown(KeyCode.UpArrow) || Input.GetKeyDown(KeyCode.DownArrow))
     {
         if (Input.GetKeyDown(KeyCode.UpArrow))
         {
             MovementVertical(1f);
         }

         if (Input.GetKeyDown(KeyCode.DownArrow))
         {
             MovementVertical(-1f);
         }
     }
 }

 public void MovementHorizontal(float moveAmount)
 {
     if (!Physics2D.OverlapPoint(movePoint1.position + new Vector3(moveAmount, 0f, 0f), whatStopsMovement1))
     {
         movePoint1.position += new Vector3(moveAmount, 0f, 0f);
     }
          SlidingBlocksHorizontal(moveAmount, moveAmount);
 }

 public void MovementVertical(float moveAmount)
 {
     if (!Physics2D.OverlapPoint(movePoint1.position + new Vector3(0f, moveAmount, 0f), whatStopsMovement1))
     {
         movePoint1.position += new Vector3(0f, moveAmount, 0f);
     }
     SlidingBlocksVertical(moveAmount, moveAmount);
 }

 public void SlidingBlocksVertical(float moveAmount, float adjustmentValue)
 {

     if (Physics2D.OverlapPoint(transform.position + new Vector3(0f, moveAmount, 0f), slidingBlocks))
     {
         while (Physics2D.OverlapPoint(movePoint1.position, slidingBlocks))
         {
             movePoint1.position += new Vector3(0f, moveAmount, 0f);
         }

         isSliding = true;
     }

 }

 public void SlidingBlocksHorizontal(float moveAmount, float adjustmentValue)
 {

     if (Physics2D.OverlapPoint(transform.position + new Vector3(moveAmount, 0f, 0f), slidingBlocks))
     {
         while (Physics2D.OverlapPoint(movePoint1.position, slidingBlocks))
         {
             movePoint1.position += new Vector3(moveAmount, moveAmount 0f);
         }

         isSliding = true;
     }

 }