Question about Using Apple Remote Desktop over the Internet

I thought if my parent's iMac connects to my home's network via VPN, their iMac will be treated as "local network" computer just as my Macbook Pro and they should see each other?

Yes... and no.

Yes, the are virtually on the local LAN and the can access resources on your home network. However, by default and not without a lot of work, the auto-discovery protocols (e.g. bonjour/zeroconf) do not reach out over the VPN link. This is, in part, because they use broadcast traffic, and the VPN doesn't pass broadcast traffic since it could overwhelm the WAN link.

Instead, you need to know the home LAN IP address assigned to their VPN connection (you can get this from the VPN server log), and then tell your ARD to connect to that IP address. Then you'll be all set.

If your MacBook Pro has an IP in the 192.168.1.x subnet, then I would expect your parent's system to have an IP address in the same subnet when they're connected via VPN.

If they're getting a different network address (10.0.8.x) then it implies they're connecting to a separate LAN at your home - as if you have one LAN for your home systems, and a separate LAN for VPN-connected hosts. Bizarre, but not impossible.

I don't know your VPN configuration to know if that's the case or not, but I'd look more closely there to see if you can identify where that 10.0.8.x address is coming from (are you sure that's their VPN-assigned address and not the actually host address in the remote network?

If I also connect to my own VPN (using loopback or hairpin NAT), I would be assigned 10.0.8.10 and from there, I can just type my parent's assigned VPN IP as 10.0.8.4 and voila, I can get the ARD working.

That indicates that the VPN is, indeed, handing out its own block of IP addresses separate from those of your LAN. I don't know the specifics of the VPN server you're using to know if that's normal/expected, but my gut reaction tells me it's not - the main point of the VPN is to connect remote clients with systems in the LAN, and if it creates a private LAN for VPN clients that defeats much of the purpose.

So I'd look more deeply at the VPN server config. Maybe that's the default block of IP addresses and it's supposed to be changed to match your LAN during the setup?

What I am trying to achieve eventually is that, my Macbook Pro does not need to connect to my own VPN. In such a case, I would get my local IP address a 192.168.x.x while my parents' iMac, for certain, would be connected using VPN and would get 10.0.8.x.

A better solution would be to get your parents' system an address in your 192.168.0.x network.

You may also be able to overcome this via routing on your host. Since its address is 192.168.0.x, any traffic for any other address is sent to the default router (which, presumably, is not your VPN server). You could tell your MacBook Pro to send traffic for 10.0.8.x to the IP address of the VPN server instead:

sudo route add -net 10.0.8 <IP of VPN server>

This command (executed on your MacBook Pro) would be transient and need to be re-entered after a reboot, but it may be worth trying to see if it works, and then you can look to automate it.

I can have my home's network and my parent's home connected using a site-to-site VPN devices and config

That would also solve the issue, and save them from having to initiate the VPN connection manually. However, having a fallback plan is advised, just for those occasions where the site-to-site doesn't work for whatever reason.

Or, I could have my parent's home Router to update the Dynamic DNS (Dyndns.org) so that they can have a hostname which I can use from my macbook pro to point to their iMac's address. Do you think it would help?

dyndns would only ever map to their public IP address and is not what you want here. Technically you could do it if you didn't mind punching holes in their NAT router to let public traffic in on the ARD ports(!), and if you didn't care about securing the connection between them and you. I highly recommend against this option.

I'd probably get a firewall with a VPN server embedded and dynamic DNS (DDNS) support, and then connect to the target firewall via VPN and screen share from there. A firewall with a VPN server will usually have a DHCP server with decent capabilities and can be configured for IP addresses assigned by MAC address, so you can establish consistent IP addresses on the target network. Bridging the networks can work with the right VPN devices and configuration, but — if you're all in the same IP subnet — now you have to coordinate IP address assignments across LANs, or migrate one or both to different subnets. I'd also use a different subnet from what's in use locally, and I'd stay out of 192.168.0.0/24 and 192.168.1.0/24 when VPNs are in use, as those are very commonly used, and VPNs are based on IP routing and IP routing doesn't work all that well with the same subnet on both ends of the VPN link.

I don't know how much you know about VPN and connecting to a remote network.

Normally when I get this problem it is because both networks are using the same IP range, for example 192.168.1.x which seems to be a default range used on many if not most home routers.

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If this is indeed the case and you enter for example 192.168.1.1 to 192.168.1.254 into the two network fields in the scanner then the network packets sent from your machine will never cross the connection to your parents house and hence will never find any equipment connected to their network.

I do not know the software you are using but unless the software solves this problem for you you will not be able to see the contents of the external network even after connecting with VPN.

Hans