Completely confused with scripts (date picker doesn't work)

Hello,

I got completely confused with scripts and how they load :( Currently, my date picker doesn't work.

I'm using latest jquery and jqueryui libraries. I load them in functions.php as following:

add_action( 'wp_enqueue_scripts', 'dlfrw_enqueue_scripts', 1 );
function dlfrw_enqueue_scripts() {

	// general jquery & other libraries include
	if( !is_admin() ){
		wp_deregister_script('jquery');
		wp_register_script('jquery', '//ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js', false, '1.9.1');
		wp_register_script('jqueryui', '//ajax.googleapis.com/ajax/libs/jqueryui/1.10.0/jquery-ui.min.js', array('jquery'), '1.10.0');
		wp_enqueue_script('jquery');
		wp_enqueue_script('jqueryui');
	}
}

When I click on the date picker, I get the following JS error:

Uncaught TypeError: Cannot read property 'msie' of undefined ui.datepicker.js:1532
$.extend._generateHTML ui.datepicker.js:1532
$.extend._updateDatepicker ui.datepicker.js:616
$.extend._showDatepicker ui.datepicker.js:582
(anonymous function) ui.datepicker.js:222
b.event.dispatch jquery.min.js:3
v.handle jquery.min.js:3

I've noticed that this erros is coming from ui.datepicker.js v1.6 script that GF loads itself. I've tried to wp_deregister_script that script, but with no luck.
How can I fix it please?

WP: 3.5.1
GF: 1.6.12

Hello,

@richardvav thank you for letting me know. I've commended out my code with custom jquery completely. So all the scripts are now coming from WP.

GF CSS in enabled. However, the datapicker doesn't have any styles still.

The staging websites is at http://gymtopia.dashaluna.com/add-story
htaccess login details (user/password): adm/adm

I would hugely appreciate any help. All seems to be working fine in the admin preview of a form, but not on the front end.

Also, is it possible to delete GF datapicker script in case when I'm adding the whole jqueryui library?

Many thanks, Dasha