Unable to access outside service from inside LAN

Assuming Spiff is correct, and your router can't handle port forwarding to the external ip from within the network there is a small work around (and it does sound like this is the case);

You can edit the hosts file, which can be found at /etc/hosts in most unix-systems and in C:\Windows\system32\drivers\etc\ on Windows.

if you add

192.168.0.15  example.com

in that file, your computer will go to the ip spesified whenever you try to access example.com. You will of course have to do this on every computer that you wish to use within the network.

You can check the wikipedia article for more details on where to find it: https://en.wikipedia.org/wiki/Hosts_file

Given that you mentioned port forwarding, I assume your home gateway is acting as a NAT -- or more specifically NAPT -- gateway. What you're trying to do is called "hairpin NAT" or "NAT hairpinning", in reference to the way a literal hair pin doubles back on itself (the same allusion is used by the term "hairpin turn" for a sharp bend where a road doubles back on itself).

Some NAT gateways are crap and don't support hairpinning. It may be time to explore your upgrade options.