Solutions which are described above, even with unique CookieFile names, can cause a lot of problems on scale.
We had to serve a lot of authentications with this solution and our server went down because of high file read write actions.
The solution for this was to use Apache Reverse Proxy and omit CURL requests at all.
Details how to use Proxy on Apache can be found here: https://httpd.apache.org/docs/2.4/howto/reverse_proxy.html