Yes, this is possible - there are a number of solutions here, none immediately spring to mind as trivial to implement though.
I'd be inclined to get a LEB (ie a low end virtual PC) with Linux and throw OpenVPN on it. I'd then set the device up so that both the home network and portable device connect to the VPN and can route directly to each other through it.
You could also set things up using port forwarding on your router - so that requests coming from the wider Internet to your router are forwarded on to the appropriate PC on your LAN. This is quite tricky and will probably require policy based routing based on the port.