@flaog - got a weird email from WordPress quoting a post from you but it doesn't appear to be where it should be.
Anyway, you wanted to know how I got the two blog pages on my site at http://www.consultyorkshire.com
It finally turned out to be quite easy using the theme Weaver which has the option to create a page-with-posts. To get 2 blog pages, you need to have 3 of these pages-with-posts. Call them P-w-P 1, P-w-P 2 and P-w-P 3.
P-w-P 1 behaves normally and shows all your posts and this is the page that you specify in the settings as your "blog" page. The trick is that you make a custom menu and don't include this page so it isn't visible.
Then you want to direct one lot of posts to P-w-P 2 and one set to P-w-P 3. In Weaver, this is also quite simple to do. P-w-P 2 can be set TO display Category X and P-w-P 3 can be set to NOT display Category X.
P-w-P 2 and/or P-w-P 3 can be displayed on your custom menu, where it will look and behave like a normal blog page as far as I can see.
The only problem now for me is that I want complete control over P-w-P 2 and I want other members of my consortium to be free to post what they like on P-w-P 3. To do this, I've got a plug-in called Restrict Categories which allows only the Webmaster to access Category X.
You can see the result of all this on my site http://www.consultyorkshire.com
Bear in mind it's a work in progress, so it looks quite bare at the moment!
The only page of posts you can see is called "Articles" and it corresponds to P-w-P 3 above. It's on the main menu along with Home, About, etc.
The top menu is a category menu - I don't know if this is WP standard or a Weaver thing. All the items there are sub-categories of the main category called "| Show Directory". This is my Category X which controls where posts go.
Hope that explains it and is helpful. If you want me to do it for you, I charge £25 an hour (40 Australian dollars). :-)