Hi there,
Wordpress has noConflict() setup for jQuery. That means, you can only utilize jQuery() and not $() directly. $() will work too if it’s wrapped by jQuery().
What you’re adding is what breaks the entire WordPress jQuery dependency, it’s not optimized for WordPress. It’s working here http://hotelcrosal.creativaimage.it/booking/widget-ricerca.html since it’s not running in WordPress platform, hence, there is no conflict.
The only solution is just making it WordPress compatible. You may want to contact a developer that could implement it for you. WordPress has prebuilt jQuery UI library too which may be conflicting with your script.
Thanks!