Apache Virtual Host not accessible from local network

Solution 1:

If you try to access the web server from inside using the outside address, your router must translate your source address too. This is called NAT reflection.

If it doesn't, the webserver sends the return traffic directly to your computer and the TCP connection can't be established because your computer talks to the outside address of the webserver and gets the traffic back from the inside address.

If the router translates your source address the webserver sends the return traffic to the router from where it gets relayed to your computer.

Using different DNS addresses inside and outside (Split DNS) as Brandon Xavier suggested in the comment would be another solution. This would not require NAT reflection.