Network mysteries and Screen/File Sharing

I purchased an iMac running Yosemite for my aging parents who live about 100 miles away, set up Screen Sharing and File Sharing and all works fine. I set up on a laptop but my main Mac is an iMac.

When I set up sharing the laptop was on their home wireless LAN and so their machine appeared in Go > Network and even though I’m back home and over the internet, it still appears in Go > Network and Screen Sharing and File Sharing works fine via this method. I don’t know how this works. I thought it was only for LAN and would no longer connect after I left the LAN.

However, there are still issues;

I can’t access the remote iMac until I phone my father and ask him to go into Sharing Settings and highlight my username under Allow access to these Users, so it changes from grey to blue. I thought it would stay activated permanently.

I can’t access the remote iMac via Go > Connect to Server vnc or afp + its IP address on the laptop or my main iMac (even though on the laptop it connects OK via Network).

Does anyone know the answers to the above? And there any way to copy the Go > Network credentials to another mac?

Are you signed into iCloud on both? Could it be “Back to my Mac”?

VNC/RDC will only work locally unless you have opened ports in the router for the server machine.

Thanks, that settles the VNC Server non-connection issues. Yes Back to My Mac must be the reason they are still connected. I thought it wasn’t an option on Yosemite but I just found it’s there and I’d switched it on for both machines. There’s so much to do do in set up and file migration I forgot I’d done it.

Mysteries Solved!