Need to set up membership site on wordpress

I have 2 sites on a wordpress network. The additional site only needs to be membership only. Not paid for membership, but group access. No registration please. Just login. There will never be payment required.

I cannot for the life of me get the membership plugin to work only on the additional site and this is what I need help with.

So to recap: The first site is freely open to the public. There is a link page to the second site which is login access only. I want all the pages of the second (membership) site to be hidden too

Can you help?