MVC Controller Class
It looks like you are trying to write object oriented code, however this is completely procedural. Remove static everywhere and use dependency injection if you want to make this OO.

Static code is hard to test. It is the equivalent of a namespaced function.

Even your new objects that you create are the equivalent of calling a function.

        case 'ControlBookmark_add': 
            new ControlBookmark('add');
            break;


I'd recommend one of the following:


Spend a long while learning how to write real object oriented code.
Give up and convert to procedural code. Skipping all of the wasted classes and new's


Some people may disagree that I would suggest moving away from object oriented code, but your code is so far away from object oriented that it makes sense to me.

Response to the Edit

It does look a bit better now.  It would be a good experience for you to unit test this with PHPUnit.  I think you would find it very hard with the static and new.  That would give you a motivation to change it further.  However, I'm guessing the testing this code will receive will be based on seeing the page on the browser, which is okay for a lot of people.

One comment on the edited version:

// Do you really need the 'remove' parameter to your constructor?
// Especially when you call the add method on it?
// Also, objects aren't that special I wouldn't bother with _instance.
$control_bookmark = new ControlBookmark();