The output of route -n without and with the VPN enabled should show what's going on.
For example if your local network was 192.168.1.0/24, you should see this line:
192.168.1.0 0.0.0.0 255.255.255.0 U 202 0 0 eth0
This tells you that the 192.168.1.0/24 network is accessed via the interface eth0.
If this doesn't appear [or points to a different interface] when VPN is enabled, that's your problem.
Exactly how to fix it... You could manually install that route, but your VPN setup should to that for you.
Hard to give more advice without knowing more - might be better to ask on your VPN forum, as this isn't
really related to TVHeadend.