Why does mysqli num_rows always return 0?

You need to call mysqli_stmt::store_result() prior to the num_rows lookup:

if($stmt = $mysqli->prepare("SELECT id, title, visible, parent_id FROM content WHERE parent_id = ? ORDER BY page_order ASC;")){  
    $stmt->bind_param('s', $data->id);  
    $stmt->execute();
    $stmt->store_result(); <-- This needs to be called here!
    $num_of_rows = $stmt->num_rows;  
    $stmt->bind_result($child_id, $child_title, $child_visible, $child_parent);  

    while($stmt->fetch()){
        //code
    }

    echo($num_of_rows);

    $stmt->close();
}

See the docs on mysqli_stmt::num_rows, it says it right near the top of the page (in the main description block).