Basically you need a solution to router the internet requests from your current computer (ouside your network), through your VPN and to your local network (and its internet access).
Using Teamviewer's VPN, you only get a direct connection between your current computer and the computer running Teamviewer (or a "private" network between them I could say). So, I believe you don't actually have access to your local network.
The only way you could have access to the internet on your network is through a proxy. The computer, inside your network, would receive requests over Teamviewer's VPN network and act as a proxy to your local network.
Here is how I accomplished that:
On the computer inside your network:
- Download and install a proxy server on your computer running Teamviewer server, inside your network. I suggest using Squid.
- Set up your proxy server and make sure it will accept all incoming requests, including from the Teamviewer VPN network (not a local network). I just gave access to "all" in "/etc/squid.conf" in the proper configuration parameters (please refer to the proper documentation).
- Initialize the proxy.
- Make sure Teamviewer is running as a service and that VPN connection is enabled.
On the computer outside your network
- Make sure you are connected through the Teamviewer VPN connection
- Go to your web browser proxy settings and set parameters same as below
- Surf the web using your private network's internet access.
proxy server: hosname or IP (you can used the IP address given by Teamviewer, but hostname is best)
connection port: 3128 (Squid's default port)
Use the same server for all protocols
PS.: You can setup a proxy server for the whole computer, using Internet Settings (IExplorer and Chrome), but Mozilla Firefox supports a "private" configuration, allowing you to surf the web via proxy only inside Firefox.