Sidebar button click redirect when user is not logged in instead displays it

when you want interaction between client side and server side you should use ajax .

i think this Link will be very helpful to you 🙂
Put this in your javascript

var data = {
    action: 'is_user_logged_in'
};
jquery.('.x-btn-widgetbar').on('click',function(){
   jQuery.post(ajaxurl, data, function(response) {
      if(response == 'yes') {
           // user is logged in, do your stuff here
       } else {
           // user is not logged in, show login form here
               window.location = <login url here >;

       }
   });
});

put this in your functions.php

function ajax_check_user_logged_in() {
    echo is_user_logged_in()?'yes':'no';
    die();
}
add_action('wp_ajax_is_user_logged_in', 'ajax_check_user_logged_in');
add_action('wp_ajax_nopriv_is_user_logged_in', 'ajax_check_user_logged_in');

Update #1 26-9-2017

and if you want widgetbar to hide you can use this jquery :

jquery('.x-widgetbar').hide();

or

jquery('.x-widgetbar').css({display:'none'});

or simplay put this in *.css file:

.x-widgetbar{display:'none'}

update#2 26-9-2017

if want only hide the widgetbar without hiding the x button it self you can replace .x-widgetbar by .x-widgetbar-inner