Restricting y-axis Player Movement

Unity Engine
1

In my 2D game, I have two player-controlled game objects and I want to ensure that they always both have the same y-coordinate. For example, if one ran into a wall, I would want the other to stop as well. I’ve tried to implement this, seen in the code below, but it doesn’t look very good in game. I feel like this should be a super easy problem to solve, but I just can’t think of a solution. Does anyone have any suggestions as to the solution of my problem (in scripting or otherwise)?

void Update()
    {
        player1y = player1.transform.position.y;
        player2y = player2.transform.position.y;
    }

    void FixedUpdate()
    {
        if (movement)
        {
            if (player1y >= player2y)
            {
                player1y = player2y;
                player1.transform.position = new Vector3(player1.transform.position.x, player1y, player1.transform.position.z);
            }

      
            if (player2y >= player1y)
            {
                player2y = player1y;
                player2.transform.position = new Vector3(player2.transform.position.x, player2y, player2.transform.position.z);
            }      
        }
2

What is the issue exactly?

3

The player movement is restricted, except when one of them hits a wall, the other stutters up and down instead of completely stopping.

4

So what happens when a player hits the wall, in code,? Movement = false?