Restricting y-axis Player Movement

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)?

Code (CSharp):

1. void Update()
2.     {
3.         player1y = player1.transform.position.y;
4.         player2y = player2.transform.position.y;
5.     }
6.  
7.     void FixedUpdate()
8.     {
9.         if (movement)
10.         {
11.             if (player1y >= player2y)
12.             {
13.                 player1y = player2y;
14.                 player1.transform.position = new Vector3(player1.transform.position.x, player1y, player1.transform.position.z);
15.             }
16.  
17.      
18.             if (player2y >= player1y)
19.             {
20.                 player2y = player1y;
21.                 player2.transform.position = new Vector3(player2.transform.position.x, player2y, player2.transform.position.z);
22.             }      
23.         }

 

What is the issue exactly?

 

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

 

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