maybe you include your scripts ui-core and picker too early. Use wp_enqueue script() to include on the right hook. You must not include ui-core, only datepicker!
example:
wp_enqueue_script( 'jquery-ui-datetimepicker', \
$this->get_plugins_url( 'js/ui.datetimepicker.js', __FILE__ ), \
array('jquery-ui-core') , 0.1, TRUE );`
any tutorials:
- http://wpengineer.com/415/use-javascript-libraries-in-and-of-wordpress/
- http://codex.wordpress.org/Function_Reference/wp_enqueue_script
- http://wpengineer.com/2028/small-tips-using-wordpress-and-jquery/
I use the datepicker on different plugins and works fine, but it is necessary, that the order is correctly.