Hey, well first off -- CONGRATULATIONS!! Cute kid
By the sounds of things, you should be able to do exactly what you're trying to do, so I'm confused.
The site you linked to above works just fine for me, and clicking on the "Photos" link takes me to a page called "pics page" which points to the file "photos_page.htm", as you want it to. In my experience with .Mac hosting, as long as all the code in your replacement file references all the assets properly, you should be in business.. I don't use Lightroom, so I don't really know how it handles that sort of thing, unfortunately.
Before posting it to your iDisk, did you try dragging the new "photos_page.htm" file onto a blank browser window to make sure that it works as expected when it's offline? Maybe there's a problem with the file itself..