How to interleave a second WP blog on my index page

I’ve seen a few posts on the subject of having two blogs on a single page, but none of them with quite the usecase I have in mind:

I host two blogs on my site, each with its own WordPress installation and database prefix, effectively completely separate. One is at host.com/blog and the other is at host.com/ with the wordpress files in host.com/wordpress.

I want the blog at host.com/ to display host.com/blog entries interspersed with its own entries, ideally with a slightly different style from the rest of the blog (harmonious, of course, but separate) on the front page, with links leading back to host.com/blog for commenting and full viewing.

I imagine that what I’d want is a way to interleave RSS feeds into my front page, but I’m not sure how to go about doing this. Googling for a combination of WordPress and Feed or RSS turns up, well, too much to be useful.

I’m willing and able to modify my CSS and theme pages, but I’d rather not muck with the WP files themselves, as I try to stay up to date.

Can anyone point me at an appropriate plugin? The one criteria I don’t see any of them meeting is the “don’t create new posts” one — they all seem to intend to create new posts in the host blog for the feed. That’s no good. That results in duplication of data, something I wish to avoid.

Thanks in advance.