bool shouldCallOtherButtonEventHandler = true;

private void OnButton1_Click(object sender, EventArgs e)
{
   if(shouldCallOtherButtonEventHandler == true)
   {
        shouldCallOtherButtonEventHandler = false;
        OnButton2_Click(null, null);
   }
   //code for the first button event handler.
}

private void OnButton2_Click(sender, EventArgs e)
{
   if(shouldCallOtherButtonEventHandler == true)
   {
        shouldCallOtherButtonEventHandler = false;
        OnButton1_Click(null, null);
   }

   //code for the second button event handler
}

private void OnButton1_Click(object sender, EventArgs e)
{
   Button1Function();
   Button2Function();
}

private void OnButton2_Click(sender, EventArgs e)
{
   Button1Function();
   Button2Function();
}