You need a plugin to do that. In file vb/ckeditor.php there's a function called setToolbar() that builds an array describing the buttons on the toolbar. At hook location editor_toolbar_set, the array is in $this->config['toolbar'] and you can change it however you want.
Since you asked for instructions every step of the way I went ahead and wrote somehting to move a button. To use this you create a new plugin using hook editor_toolbar_set and this code:
Code:
$insert_after = 'JustifyLeft'; // change this if you want it somewhere other than after JustifyRight
$move_button = 'justify'; // change this to 'title' of your bbcode
foreach ($this->config['toolbar'] AS &$row)
{
if (!is_array($row))
continue;
if (in_array($insert_after, $row))
$insert_row = &$row;
if (in_array($move_button, $row))
$remove_row = &$row;
}
if ($insert_row AND $remove_row)
{
$offset = 0;
foreach($insert_row AS $val)
{
$offset++;
if ($val == $insert_after)
break;
}
array_splice($insert_row, $offset, 0, $move_button);
if (($k = array_search($move_button, $remove_row)) !== FALSE)
{
unset($remove_row[$k]);
if (($last = array_pop($remove_row)) !== '-')
array_push($remove_row, $last);
}
}
and as mentioned in the comments, you would want to change $move_button to the title of your bbocde (unless it happens to be 'justify'), and also change $insert_after to the name of the button you want it to be after (the justify buttons are JustifyLeft, JustifyCenter, and JustifyRight. If you want it somewhere else you can look in the ckeditor.php file I mentioned and you can probably figure out the name for each of the buttons).