calll login from a js script

Stefano,

You can try the code below. What it does is first open the dialog and then sends the AJAX request.

$('#ajax-login-register-login-dialog').dialog('open');
                $.ajax({
                    type: "POST",
                    url: _ajax_login_settings.ajaxurl,
                    data: {
                        action: 'load_template',
                        referer: 'login_form',
                        template: 'login-form',
                        security: $('#ajax-login-register-login-dialog').attr('data-security')
                    },
                    success: function( msg ){
                        $( "#ajax-login-register-login-target" ).fadeIn().html( msg ); // Give a smooth fade in effect
                    }
                });

You can also reference these lines of code in GitHub

https://github.com/zanematthew/zm-ajax-login-register/blob/master/assets/login.js#L95

https://github.com/zanematthew/zm-ajax-login-register/blob/master/assets/login.js#L105