Woocommerce checkout update totals with datepicker

Try wrapping the trigger in a standalone callback.

jQuery(function() {
    jQuery( "#datetimepicker" ).datetimepicker({
        onClose:function(ct,$i){
        my_callback();
        }
    });
    function my_callback() {
        jQuery( 'body' ).trigger( 'update_checkout' );
    }
});