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A webpage can rank for more than one keyword and that's a good thing. Having the low volume keyword ranking well wouldn't hurt the main keyword's ranking. However it could be that Google's algorithm decided that the page is better suited for the lower-volume query. I would take another look at the page, including links and citations and see if you see something there. For the homepage issue, it still sounds like a subdomain issue, especially because you see it when you search the root domain, but not the www subdomain.