Hi Kelly,
I don’t think there’s an easy way to do that. I assume you want to show a mashup from the POIs in the other database?
If you just want to show a map (or mashup) from site #2, then you could perhaps use an iframe. Embed an iframe in a page on site #1 with its source pointing to a post/page in site #2. In site #2 use a post template that doesn’t have a header/footer/sidebar, to show just the map.