How do I keep child object from sliding away from parent as the parent moves?

It seems that Ball is a Rigidbody.

You should not nest multiple Rigidbody or move a parent of a Rigidbody at all.

Rather use a FixedJoint.

Afaik you can simply do something like

private Rigidbody miffyRigidbody;
private FixedJoint BallFixedJoint;

void OnTriggerEnter(Collider collider)
{
    isColliding = true;
    if (collider.CompareTag("Player"))
    {
        miffyRigidbody = collider.attachedRigidbody;
    }
}

void OnTriggerExit(Collider collider)
{
    if (collider.CompareTag("Player"))
    {
        miffyRigidbody = null;
    }
}

private void Update()
{
    if(miffyRigidbody && Input.GetKeyDown(KeyCode.P))
    {
        if(!BallFixedJoint)
        {
            BallFixedJoint = Ball.GetComponent<FixedJoint>();
            if(!BallFixedJoint) BallFixedJoint = Ball.AddComponent<FixedJoint>();
        }

        BallFixedJoint.connectedBody = Miffy.GetComponent<Rigidbody>();
    }

    if(Input.GetKeyUp(KeyCode.P))
    {
        if(!BallFixedJoint)
        {
            BallFixedJoint = Ball.GetComponent<FixedJoint>();
            if(!BallFixedJoint) BallFixedJoint = Ball.AddComponent<FixedJoint>();
        }

        BallFixedJoint.connectedBody = null;
    }
}