problem on my WordPress site

Hello ! I have a wordpress site, in our site I use two different theme, the first for the public homepage and the second for it is a private site that is to say the user can not access the private site to create an account on the first site, and maintenanet I find problem, how can view the two themes on a site and a domain name and how can manage user accounts to better explain the site
when you tap www. ***. com /
the site display the public home page, there is button register and login
if the user enters the login and password the site directed to the private site
thank you for understanding and for helping you