It is easy to share Google Sites (and Google Docs and Calendar) with Google Groups in a secure manner. All you need is the Google Groups' email address shown at the bottom of your Group Home page.
In Sites, you can invite a Google Groups email address to your site as owner, editor, or viewer. Only people who are part of that Google Group will be able to access the Site in the way you share it, and as the membership of the Google Group updates, the access to the Site updates with those changes.
In Docs, you can set the sharing setting of your Doc or uploaded file to private, and then add the Google Groups email address with either edit or view access. In a similar way, as the membership of the Google Group updates, the access to the Doc or uploaded file updates with those changes.
In both cases, someone who gets the link but isn't a member of the Google Group that received the sharing privileges won't be able to access the Site or Doc, unless you specifically give them access, too.
You can set up a group so that people can ask to join it. Once their membership has been approved, they will have access to anything shared with that group.
If you are a member of a group and the group has access, the site will not appear in 'my sites' but you will still have access to it
Here are a some Help Center articles that could help you.
There is a thread here that discussed issues surrounding access control. I have copied a post by 'smmo' from that thread which I hope will prove a useful case study for others
I don't know how others may handle this. But, here's what we do: If a member needs to contact me as administrator, they send an email to me directly. If they want to ask a question or send info to all 200+ members, they send an email to the Group email address, which automatically goes to everyone. I have a note on our Sites home page with a hyperlink to my administrator email.
Do they log into Sites or Groups to view information online? Do they ever visit the Group page? Short answer: They log into Sites to view our online info. They only would visit the Group page if they want to view the group email archives. FYI: If you aren't going to use the group email feature, they would never need to visit the Group page. Long answer: Now that I've moved all our pages and files to Sites (since Google is discontinuing Groups pages & files), my users go to the Site for our online content. They no longer go to Groups, unless they want to look through our group email archive. I have a page on the Site called "Group Emails" with instructions about how we send/receive Group emails and a hyperlink to the Group URL in case they want to view the archives. So, they don't have to know how to get to Groups, just our Site. Now when new members join our organization, I add them to the Google Group, which automatically shares the Site and Calendar with them. I send a welcome email separate from Google with various instructions and information including how to set up a Google Account, how to use our Group email distribution, and how to access the Site. I no longer give any instructions for accessing the Group page, as they really don't need it and I don't want to confuse them. I just want them to go to the Site for everything. My message for the email they receive when I add them to the Group says "Welcome to the ___ Google Group. Please follow the instructions in the separate email I sent you. my name"
I assume you have the calendar displayed on your site so they don't have to visit Google Calendar separately? Correct. I created a page titled "calendar" and imbedded the calendar in it. This is actually an improvement over Groups, where I had a page titled "calendar" but could only include a hyperlink which would take them to the Calendar.
Do you also have a Docs account or are you storing all files on Sites? I use the Files feature on Sites.
I'm trying to understand what this looks like on the user side of things. I may use our Google resources differently than you might want to. Our organization wanted a private way to do four things: 1-allow members to send emails to all 200+ members by using only one email address (which is what Google Groups does) 2-share recommendations for services, contractors, medical providers, etc (which we used to do through Google Group Pages and now do on Sites pages) 3-share our membership roster and various Word and Excel files (which we used to do through Google Group Files and now do in Sites files) 4-share an event calendar (which is now imbedded in Sites).
For the administrator, managing users is very easy in Groups. I only had my Site a few weeks before Google changed the sharing interface, but even the "old way" wasn't as easy as Groups. In Groups, you see a page of user email addresses at a time, sorted alphabetically. It shows you if emails are bouncing. It shows you how the members are subscribed to emails. It has an "edit" button next to each email address, which lets you change their type of subscription. There is also a search bar, so you can enter a whole or part of an email address and immediately find a user - a great feature if you have hundreds of members, as you don't have to scroll through the full list. You can easily unsubscribe members. If you need to change a member's email address, you unsubscribe their current email address, then subscribe the new email address. I do maintain a membership roster in Excel. I check it against the Google Group listing occassionally because Google does NOT notify administrators when users unsubscribe themselves.