Mac – Screen Sharing over internet on OS X Lion – cannot control remote machine

Since the Screen Sharing feature seems to be the only one unable to connect, the best way to diagnose its behavior is by using the application directly.

Please, launch screen sharing located in:

/System/Library/CoreServices/ScreenSharing.app

The application has no visible "UI" so don't expect a fancy Cocoa interface. Instead, once you have loaded it, all you'll see is this "poor" icon in the Dock:

Click on it and then go to Preferences in the Mac menu bar. You should be presented with:

Notice the second option to only encrypt passwords and keystrokes. That's fine, but as you can see, there's no option to skip encryption altogether. Some VNC versions have incompatibilities with encryption, but this would be rather shocking since you're talking about OS X vs OS X.

In any case, once you have the settings like that, try connecting, again, in the menu bar: Connection -> New (or ⌘cmd + N).

A simple dialog appears asking you to enter the Host's name. Following your screenshots, try: 192.168.1.99 and hit enter.

We'll see what happens from here. Also, have the Console.app open on both computers, to see if there are any System messages going on (or anything related).

Apple Remote Desktop will involve either having a VPN or open ports and static IPs. I think you will be much better off with LogMeIn.com's free version, which will require zero intraction from your family members and open ports are not necessary. You will need to know a user's credentials on their computer. If they require more privacy they can disable LogMeIn from the menu bar item, as it will always be on as long as they are connected to the Internet. I suggest adding a user to each computer with your name and one password—that will be one less thing for you to remember and if they change their password or don't remember it you can still help them.

I use both ARD and LogMeIn daily, but ARD is more than you need.