Hi firsttimezenphoto-
First of all: even though your other post says you're using Gallery 2, I'd try this out and switch back to ZenPhoto. It's so much friendlier to use!
I encountered your same problem when I set zenphoto up on my Dreamhost server recently. I had .htaccess uploaded, ran setup.php (everything checked out "green" there), was using mod_rewrite, had the RewriteBase set correctly, and still encountered your symptoms. Basically, I was in your same exact position: ZenPhoto just kept sending me to /zp-core instead of /photos/zp-core.
The solution for me: Edit your zp-core/zp-config.php file. Down at the very bottom are two commented out lines that are marked for "ONLY IF YOU'RE HAVING PROBLEMS". Well, I was

I uncommented the first line and set it for my path, and all now works well:
// Uncomment the following two lines ONLY IF YOU'RE HAVING PROBLEMS,
// like "file not found" or "not readable" errors.
// These allow you to override Zenphoto's detection of the correct paths
// on your server, which might work better on some setups.
////////////////////////////////////////////////////////////////////////////////
define('WEBPATH', '/photos');
// define('SERVERPATH', '/full/server/path/to/zenphoto');
I hope that helps!