Internal and External Domains

I’m in need of help.
Where I work they wanted to setup a blog. Our systems run 4 HTTP servers in the production environment, 2 internal and 2 external, load balanced of course.
#So we have blog.int.dude.com (The domain dude.com isn’t real, I am hiding what the domain is for now since the site isn’t going to be accessible by external users, and I don’t know if I’m allowed to reveal my company’s domain right now). for the internal site running on Web1 and Web2. I installed wordpress here, and its running very well, small problem with images not being rendered in wordpress, but the CSS, and the site seems to be functioning.
#then we have blog.dude.com running on web3 and web 4, and it connects through our DMZ into our internal network for the mysql server. However blog.dude.com can kinda load, but its looking to blog.int.dude.com for the css files and all that. I need it to refer to its own external servers, and stop trying to get into the internal webservers.

Both sites are exactly the same except for subdomain. Can you please help me, and feel free to ask questions to clarify anything that isn’t easy to understand.