MoveTowards and Lerp not working on RectTransform?

Hello i am currently working on a menu, so we are talking GUI elements, where when you click on one folder the others move away, so there is room for the chosen folder to open. But i cannot find out how to smoothly move the folders around. I have tried using MoveTowards and Lerp, but it does not work. I have left my code both for Lerp and for MoveTowards so you can see. Note This code is run in a coroutine.

 //if the folder is not open...
 if (!isFolderOpen)
 {
     //Check every RectTransform in the children list...
     foreach (RectTransform child in children)
     {
         //and check if it's x position is bigger then the currently clicked folder
         if (child.anchoredPosition.x > rect.anchoredPosition.x)
         {
           newPos = new Vector2(child.anchoredPosition.x - distance, child.anchoredPosition.y);
 
             while (child.anchoredPosition != newPos)
             {
                 //child.anchoredPosition = Vector2.MoveTowards(child.anchoredPosition, newPos, 10 * Time.deltaTime);

                 //child.anchoredPosition = new Vector2(Mathf.Lerp(child.anchoredPosition.x, child.anchoredPosition.x - distance, 0.5f), child.anchoredPosition.y);

                 yield return null;
             }

Update I can now make the folders move, but the movement is not stable. The first couple of times you open and close the folders everything looks great, but after a couple of clicks, the folders start shaking and suddenly move out instead of in. Here is the new code:

 private IEnumerator MoveOut(RectTransform folder, bool left) //Moves the folders outwards away from the selected folder
 {
     //Creates a variable to store the new position of the folder
     Vector3 newPosChild;

     //should it move left?
     if (left)
     {
         //then set the new position to it's current position minus distance
         newPosChild = new Vector3(folder.localPosition.x - distance, folder.localPosition.y, folder.localPosition.z);
     }

     //or should it move to the right?
     else
     {
         //then set the new position to it's current position plus distance
         newPosChild = new Vector3(folder.localPosition.x + distance, folder.localPosition.y, folder.localPosition.z);
     }

     //As long as the folder is not in it's new position...
     while (folder.localPosition != newPosChild)
     {
         //move it towards it's new position
         folder.localPosition = Vector3.MoveTowards(folder.localPosition, newPosChild, movementSpeed * Time.deltaTime);

         if (Vector3.Distance(folder.localPosition, newPosChild) < 10)
         {
             folder.localPosition = newPosChild;
         }

         yield return null;
     }
 }

 private IEnumerator MoveBack(RectTransform folder)
 {
     StoreOriginalPosition childOriPos;

     childOriPos = folder.gameObject.GetComponent<StoreOriginalPosition>();

     while (folder.localPosition != childOriPos.originalPos)
     {
         //move it back to it's original position
         folder.localPosition = Vector3.MoveTowards(folder.localPosition, childOriPos.originalPos, movementSpeed * Time.deltaTime);

         if (Vector3.Distance(folder.localPosition, childOriPos.originalPos) < 10)
         { 
             folder.localPosition = childOriPos.originalPos;
         }

         yield return null;
     }
 }