Hosting WordPress on backend machine

Hi, I need help with setting up WordPress on a backend server.

I would like to WordPress to be accessed by https://www.mycompany.com/blog/ where /blog is redirected to a separate machine (can be only internally accessed only).

I have set ProxyPass on the web facing machine as follows:
ProxyPass /blog/ https://192.168.0.100/wordpress/
ProxyPassReverse /blog/ https://192.168.0.100/wordpress/

So far so good. So when a web user clicks the above link, he is taken to the WordPress Blog – which is great.

However, the problem starts from here on. All the links on the WordPress blog are pointing to https://192.168.0.100/wordpress/?p= etc. which are obviously not available from the web. I tried to change the blog URL in WordPress (General Settings) to https://www.mycompany.com/blog/ but that ends up in a loop as the web facing machine resolves it and sends it to the backend machine which in turn sends it back to the front machine and so on.

I have looked at the forums but am unable to locate a solution that will work. Hope someone out there has got it working.

Many thanks. Any suggestions will be greatly appreciated.