Dealing with a library that depends on jQuery

First of all if you investigate PikaChoose source code, then you will see that it wraps the code with self invoking closure:

(function($) {
    // ...
})(jQuery);

It means that they use short form properly. In the same time it means that all you need to do is to enqueue jQuery and PikaChoose scripts and it will work fine. You can do it by writing your own hook for wp_enqueue_scripts action:

add_action( 'wp_enqueue_scripts', 'wpse8170_enqueue_scripts' );
function wpse8170_enqueue_scripts() {
    wp_register_script( 'pikachoose', '/path/to/pikachoose.js', array( 'jquery' ), null, true ); // register pikachoose script
    wp_enqueue_script( 'wpse8170-my-custom-js', '/path/to/my.js', array( 'pikachoose' ), null, true ); // enqueue my.js and pikachoose scripts
}

Pay attention: do not enqueue 3rd party libraries, just register it and use it as dependent library when you enqueue your custom javascript file.

Your my.js should look like this:

(function($) {
    $(document).ready(function() {
         $("#divID").PikaChoose();
    });
})(jQuery);