I found the solution by myself.
To anyone that is having the same problem, rather than remove_meta_box and add_meta_box, simply include this:
// Global the $wp_meta_boxes variable (this will allow us to alter the array)
global $wp_meta_boxes;
// Then we make a backup of your widget
$my_widget = $wp_meta_boxes['dashboard']['normal']['core']['{widget id here}'];
// We then unset that part of the array
unset($wp_meta_boxes['dashboard']['normal']['core']['{widget id here}']);
// Now we just add your widget back in
$wp_meta_boxes['dashboard']['side']['core']['{widget id here}'] = $my_widget;
inside a function and ‘add_action’ with ‘add_meta_boxes’ hook.
I find this here.