Smart Search Boxes can perfectly co-exists. There is something about your settings and the way it is confgired. I suggest to disable home page smart search box, add a new one with default settings, define Search URL and start testing. Copy settings (one by one) from existing smart search box (not working one) to the test one and do testing.
P.S. Probably your
Search results page URL of web part is not set correctly. By default it is
~/SpecialPages/Search.aspx. It points to URL of the page where the search results are displayed. This page must contain either the Smart search results or Smart search dialog with results web part. If empty, the current page is used.