How to keep user logged in when i have a switch language

Question

I am logged in my website e-commerce, and when I switch language: to Catalan for example, I lose my connection to the account,

I'm trying to keep the current account session with my rticles in my cart.

In fact, if i do it on normal browser, and i switch from language to another, all is good,

but the problem comes when i work on the private browser,

and here is my code in script,

function changeLang(culture, subdomain) {
       var url = window.location.href;

       var alternate = $('head').find('link[rel="alternate"][hreflang="' + culture + '"]');
       if (alternate && alternate[0]) {
           url = alternate[0].href;
       }
       else {
           var hostName = window.location.hostname.replace(window.location.hostname.split('.')[0], subdomain);
           url = url.replace(window.location.hostname, hostName);
       }
       createCookie('IdKids.Culture', culture, 180);
       window.location = url ;

   }

 

so how can i fix this problem, to keep my current connexion ?