Private Site and SSL

Hi,
I’m having a problem when I activate the Private Site: We are running a SSL-enabled site, but when entering our site-address without the https:// it goes to login page as it should but the redirect only says https:// e.g:

I’m entering https://mysite.url in the browser. Because of Private Site it goes to login-page as it should but now the URL is:
https://mysite.url/wp-login.php?redirect_to=http%3A%2F%2Fmysite.url%2F&reauth=1

and the I’m ending up in a login loop because of the http – it should be https.

It works fine if I at first call my site with https://mysite.url.

Can you take a look at it please?

Thanks in advance

/Kim