How to map from a subdomain to my main domain "blog" folder

I have isolated my WordPress blog by installing it in a different server. I use a reverse proxy technique to view the blog from my main site when the blog is running on the other server. All my URLs of the blog should start with the main site domain name.

For example:
my main site is – http://www.test.com
My blog is hosted on – blog.test.com

I use multisite, so my domains are something like:
(UK) http://www.test.com/blog (should map to) blog.test.com
(DE) http://www.test.com/blog/de (should map to) blog.test.com/de/
(NL) http://www.test.com/blog/de (should map to) blog.test.com/nl/

I’ve set up everything, but my blog (on the subdomains) uses “blog.test.com” as its main URL – it uses it for all its URLs on menus, comment form actions, etc. When I view the blog and check the inside URLs all of them are starting with blog.test.com.

My simple question is: how do I instruct WordPress to use http://www.test.com/blog/ instead of http://blog.test.com ? Likewise, http://www.test.com/blog/de/ rather than http://blog.test.com/de/

Again, my URLs actually work, thanks to reverse proxy, but WordPress needs to be instructed to “use” my main domain URL.

Can I use Your plugin http://wordpress.org/plugins/wordpress-mu-domain-mapping/ to change my internal URLS to the correct one.
According to your instructions the mapping domain will be http://www.test.com/ but what will happen to the “/blog/” folder that I want inside the main domain? Can I use http://www.test.com/blog/ as my main domain?

OR – if the above is not possible with the plugin – I’d very much appreciate if you could instruct me on how I can do this via my own, small plugin or code update, simply to override WordPress’ URLs? If you could point me to which part of your code actually does this override, that would really help.

Many thanks in advance

https://wordpress.org/plugins/wordpress-mu-domain-mapping/