Two wordpress installed seperately in with core site

Hi I am using my own custom site built in PHP and I have installed two seperate wordpress in my site for example https://www.mysite.com/blog
and second is https://www.mysite.com/forum. I have a login in my site https://www.mysite.com/login.php.

I want to how can I be able to login from my core php script to my https://www.mysite.com/blog and https://www.mysite.com/forum site simultaneously.

please suggest