In ISPC2 websites must be configured for one address or another not both. Apache has the ability to do this but that would require Apache and the site to listen on all addresses. If you were to change these settings manually then the next time you make a change in ISPC2 your changes would be over written.
If what you are trying to accomplish is to have access to the website that has a public address from your private network then this is a function of your firewall/router not the web server.
The example below shows a small map of data flow and the path that your connections would make.
Private network | Firewall/router | Public network | ISPC Webserver
10.0.0.24 --> 10.0.0.1/18.104.22.168 --> 22.214.171.124 --> 126.96.36.199
In all accounts the above example should work.
Can you show us how you have configured your server using the example above?
No real addresses please.