Sharing directories in a user’s home directory is a real hassle. Your best bet is to create a new FTP user and then change ownership of site2. This is why I create a new user for each domain I manage. Now you just need two FTP profiles depending on which site you want to FTP to.
Go to the Panel for Users -> Manage Users and Add a New User.
Once that’s done, go to the Panel for Domains -> Manage Domain and click Edit for site2. In the Fully Hosted section up top, use the dropdown menu for Users/Files/Paths and select your new user. A checkbox will appear asking if you want to move all files.