If WP is in the 'blog/' directory its going to want that 'blog/' in the URL.
I think there are some things I don't understand about your what you are trying to do.
1) Are you linking from the main site to the blog?
2) Are you linking from the blog to the main site?
3) What is generating these links?
Not to be paranoid, but I worry about the way your site includes files. I've been able to get some interesting results by playing with the URL, though I haven't got to anything critical yet I'm pretty sure I could. Try this for example:
http://twdot.w1host.com/index.php?s=blog/wp-config.php); %00
That really shouldn't happen. (You'll have to copy the whole line to get it to work.)